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Hal is referring to the fact that the office he's in is decorated with art by Frederic Remington (1861-1909), an American painter who work can be seen online here.
A type of knot used to tie a necktie
Hal's full first name is given for the first time.
A fictional town just west of Boston, which exists where parts of the real town of Brighton and the Boston neighborhood of Allston exist in reality. There used to be a real Enfield in western Massachusetts but it was disincorporated in 1938.
Organization of North American Nations Collegiate Athletic Association -- presumably the future complement of the NCAA.
"A benign encysted tumor of the skin, esp. on the scalp, containing sebaceous matter; a sebaceous cyst" (Random House Unabridged Dictionary)
Randolph Tennis Center
The Randolph Tennis Center is a real place, near Tucson, Ariz. and the main campus of the University of Arizona.
El Con Marriott
"El Con" is short for "El Conquistador," and while there is a Hilton El Conquistador Hotel in Tucson, the Marriot has a different name.
"...the fat women in the Viking hat having sung..."
Another way of saying, "It ain't over till the fat lady sings." This expression refers to opera, particularly those by Richard Wagner.
Out of eight people in the room (including himself, three deans, the Director of Composition, deLint, and C.T.), five are looking at Hal. Hal not being able to look at himself, two people are not looking at Hal, presumably deLint and C.T.
Presumably Edmonton, AB.
Spots of color.
A circumflex is a diacritical mark, as seen in the French verb être (to be). Presumably, the dean's eyebrows have taken on this shape.
The Pacific 10 athletic conference, the other members of which are: Arizona State Univ., Univ. of California at Berkeley, Univ. of Oregon, Oregon State Univ., Stanford Univ., UCLA, USC, Univ. of Washington, and Washington State Univ.
"Kekuléan" is not a type of knot. To Hal, the knot he is focusing on resembles the, self-consuming, annular shape of the snakes that inspired August Kekulé's discovery of Benzene's molecular structure. August Kekule (1829-1896), a renowned German organic chemist was the principal founder of the theory of chemical structure. His most famous work, the discovery of Benzene molecule's structure, is said to be inspired by a dream. "Kekulé's Dream" was that of a self-devouring snake, the shape of which, he used to describe the Benzene Ring.
Hal's intense focus on this annular, or ring-like, part of the tie is the first reference to annular shapes.
This word, not found in dictionaries, would seem to mean "of or pertaining to an aviary," an aviary being where birds are kept.
Judging from the way the words sound when spoken.
"Marked by conciseness, precision, or refinement of expression: lapidary prose" (thefreedictionary.com)
This terms describes a school of thought that there are rules of grammar that should be obeyed and taught. Wallace is firmly in this school.
Named for Jean Baptiste Joseph Fourier (1768-1830), a French mathematician, a Fourier transformation is "a certain linear operator that maps functions to other functions" (Wikipedia). Post-Fourier would refer to those transformations that came after Fourier.
Approximating reality using holograms
Inactivity resulting from a static balance between opposing forces 
Named for Richard Merett Montague (1930-1971), an American logician, this is an approach to semantics that suggests that the semantics of natural languages is essentially the same as those of formal languages, such as logic or computer programming.
Modality, in linguistics, refers to sign theory. Physical modality would, therefore, be either how a physical thing is represented by a sign or how any idea is represented by something physical.
Third-level, after primary and secondary
The era of the reign of Byzantine Emperor Justinian I (reigned 527-565)
Italian for "below." Particularly when used in the phrase, "sotto voce," it means speaking in a low voice, under one's breath.
Oxbridge refers to the two oldest colleges in the U.K., Oxford and Cambridge. The Quadrivium are the four academic subjects of arithmetic, geometry, music and astronomy. The Trivium are three disciplines, i.e., grammar, logic, and rhetoric.
Enlarged through strength training, specific to human muscles (see, contra, atrophied)
A neologism, meaning infused with insignia (a distinguishing mark or sign, many graphic logos are insignia)
North American Associaton of University Professors, the presumed follower to the American Assocation of University Professors.
French: from me
"...who use whomsoever as a subject..."
"Whosoever" would be the proper subjective form of this word. Hal is saying that the Deans, even with their limited grammatical abilities, would find the recent essays appalling.
one hip lower than the other
The smallest networks of blood vessels, where arteries turn into veins
As if eliminating solid bodily waste
A mafia boss
An acronym for the Racketeer Influenced and Corrupt Organizations Act, a statute used primarily to charge organized crime figures in criminal conspiracies.
relating to the practice of favoring relatives or friends
Named for Sir David Brewster (1781-1868), Scottish scientist; the angle at which non-polarized light striking a surface will reflect polarized light. Presumably a desk lamp is positioned at such an angle. For more.
A suburb of Boston, about 17 miles west of the city
Hal's older brother and the middle name of Hal & Orin's father, James O. Incandenza, literally "a tree" or "pale."
a brand name of rotary tiller
Children's clothing bearing Winnie-the-Pooh cartoon images or graphics, presumably pajamas in this instance
Literally "old-eyed," this is the inability to focus one's eyes as one grows older
A Wallace neologism (and portmanteaux) to describe the effects (shaking hands) of prolonged operation of a Rototiller
adj., biting, stinging, sarcastic
adj., straight or true; in line with
an idea represented by a shape, e.g., a stop sign, known by its eight-sided configuration
Søren Aabye Kierkegaard was a 19th century Danish philosopher and one of the progenitors of existential philosophy
Albert Camus was a 20th century Algerian-born French author of existentialist texts.
Dennis Gabor, born Gábor Dénes, was a 20th century Hungarian physicist who invented holography, for which he received the Nobel Prize.
"...Hobbes is just Rousseau in a dark mirror..."
Thomas Hobbes (1588-1679) was a British philosopher and author of Leviathan. In it, he suggests that the only escape from living in a state of nature that is "solitary, nasty, brutish, and short" is to build societies. Jean-Jacques Rousseau (1712-1778) was the Swiss-French philosopher who wrote The Social Contract, in which he advances the same argument but idealizes the state of nature.
Georg Wilhelm Friedrich Hegel (1770-1831) was a highly influential German philosopher.
Latin for "creation," the line over the a indicates the vowel is pronounced as in "hate" rather than in "father."
v. tr., "To restrain or immobilize (a person) by binding the arms" (thefreedictionary.com)
an in-laid wood pattern, often a block-pattern, typically in flooring
A brand of shoes, generally pricey.
a wrestling hold with the offensive competitor's arm wrapped under the opponent's arm and over the opponent's neck from behind, allowing an opponent to be immobilized or levered from behind
The Heimlich maneuver, named for contemporary American physician Henry Jay Heimlich, dislodges food from a choking person's trachea by applying sharp pressure to the abdomen.
This is the plural of pase, a Spanish word used in bullfighting to denote the movement of the matador's cape in drawing in the bull.
lying on one's back
a word used to denote a type of military gunfire. A formation or position is "in enfilade" if weapons fire can be directed along its length. For instance, a column of marching troops is enfiladed if fired on from the front rather than the side.
Synechdoche for the the fictional "WhataBurger Southwest Junior Invitational," an annual juniors' tennis tournament held in the novel in Tucson, AZ. (A Corpus Christi invention, Whataburger® is a well-established local burger chain in Pheonix (with 28 franchisees in AZ in 2009) but whose real fan base hails from Texas.)
shoes popular in Latin American with rope for soles
plural of cirrus, a type of cloud
a strict disciplinarian
Named for Ernst Mach (1838-1916), a Bohemian-Austrian physicist, the mach unit is a unit for the speed of sound. "Ultra-mach" would apply to a plane flying at several times the speed of sound.
This word refers to "aged and weathered boards, esp. those salvaged from dismantled barns" (Random House Unabridged Dictionary).
Employing the nautical term for "right" (starboard), the woman referred to tends to move right as she tries to move forward.
excessive or abnormally large growth in humans, also giantism
having the qualities of a parody
one subject to infantophilia (see pedophilia), but may simply reference the earlier Inner Infant group
a neologism meaning "of or like an incision"
Wallace neologism describing a smallness or absence of fingers or hands
An Incandenza family nickname for Hal's father, James O. Incandenza; the first reference to James O. Incandenza in the novel
"...Donald Gately and I dig up my father's head..."
See Hamlet, Act Five, Scene One.
At the time this novel was published, Venus Williams would have been sixteen years old.
Dymphna was a 7th century Irish saint. Her feast day is May 15. She is the patron saint of mental illness professionals, epilectics, and the mentally ill, among others.
Petropolis is Greek for "city of stone" or "city of Peter." Petrópolis is a city in Brazil near Rio de Janeiro. A treaty was signed there on November 11, 1903, ending hostilities between Bolivia and Brazil.
"Kahn" is a variant on the Jewish name for a priest, i.e., kohen.
the cause of a disease
Socratic method a technique of teaching by asking students questions, attributed to Socrates' pedagogy in ancient Greece
O.E.D. VI's count
This is a reference to the Oxford English Dictionary, sixth edition.
still in use, as distinct from those dictionary words considered archaic and not part of the modern language
deriving from Latin
deriving from Old English
Wallace neologism for "bitten to the quick", as in nails gnawed down to where they emerged from the fingertips
the sound of a Spanish-speaker's pronunciation of "you"
a little over seven ounces
"...using just audio..."
The implication here is that in the time of the book, there are videophones.
A part of Boston proper, west of downtown and across the Charles river from Cambridge. The fictional Enfield most likely occupies part of what is in reality Allston.
generally high-quality marijuana, containing a high volume of resins where THC in marijuana plants is produced
vernacular, arguably offensive, term for a cleft lip
"Teleputer", as used elsewhere in the text. Assumed to be a hybridized communications/entertainment device.
to become master over one's addiction, in this case, to end the addiction to marijuana
used as a verb, communicating with the office via modem, an early but ubiquitous tool for transmitting data between servers and client/servers.
electronic note, likely not a literal reference to an actual electronic communication, conceived in the pre-Internet era
a member of the Royal Canadian Mounted Police, their equivalent of the FBI
Porter Square, Cambridge
a neighborhood of Cambridge bordering on Somerville, about a mile from Tufts University, which is on the Somerville/Medford border
Experiencing convulsions, violent involuntary physical shaking
This would presumably be a festival celebrating the plays of German playwright Benjamin Franklin Wedekind (1864-1914), a proto-expressionist.
greedy and forceful in capturing and consuming
inflammation of the pleurae, the membranes surrounding the lungs
A television-based home entertainment system, ubiquitous in the time the novel is set, which plays copy-protected "cartridges" custom-ordered by viewers, invented by Noreen Lace-Forché
with intense attention to
See Interlace viewer, above
an episode of debauchery, engaging in excessive, pleasure-seeking, often sexual- or drug/alcohol-related
about 4.2 ounces
of low character and lacking integrity
Ernest Anthony Puente, Jr., an internationally known Puerto Rican jazz musician.
Marlborough Street runs through the Back Bay area of Boston.
taking something as one's own, without permission
As the endnote on p. 983 tells us, this the chemical name for crystal meth. Calling to mind that Infinite Jest was published in 1996, don't think crystal meth is a new phenomenon.
a mixture of varying style or content
typo or intentional misspelling of majuscule, an initial capital letter, often large-type to introduce a section of written material; Wallace's use of the noun in a verb form is likely a neologism (especially if the alternate spelling is retained)
about 1.75 ounces
grown in water without soil
a drinking mug
E.W.D. land barge
perhaps "Enfield Waste Disposal"; a garbage truck
biased from a male point of view
half a meter
nearly 20 inches
Short for "carburetor," just as the carburetor in an internal combustion engine mixes air with gas to allow combustion, the carburetor on a water pipe allows one to draw air in with marijuana smoke.
slanted, like an acute or obtuse angle, not a right-angle
Combination television and computer, generic term for an Interlace player, see also TP
correspond with; match up
indirect or dishonest