Chapter 1:
Geographical:
'Its extreme downtown is the battery': Battery Park, at the southwest end of Long Island
'Corlears Hook to Coentie Slip'
'the valley of Saco'
'marvels of a thousand Patagonian sights and sounds': The Patagonians were the South Americans

Literary and Otherwise:
'hypos': is related to emotions, depressions.
'Cato throws himself upon his sword': Cato was the hero and title character in a 1713 play by J. Addison
'belted round by wharves': a wharf is a construction built for docking boats.
'the poor poet of Tennessee'
'the story of Narcissus'
'a strong decoction of Seneca and the Stoics': Decocting is boiling down something to strengthen the flavor. Seneca and the Stoics are philosophers.
'the two orchard thieves': Adam and Eve
'the Pythagorean maxim'
'and, mid most of them all, one grand hooded phantom, like a snowdrift in the air': This seems ambiguous to me, but it might refer to Moby Dick. It might be unrelated.

Chapter 2:
Geographical:
"one of the Moluccas": The Moluccas are a arcapelago inbetween Celebes and New Guinea. It includes the Halmanera island.

Literary and Otherwise:
"Tyre of this Carthage"
"grapnels": A grapnel is a small anchor with several claws.
"ashes from that destroyed city, Gomorrah"
"Black Parliament sitting in Tophet": Tophet is from toph, drum. It is a place where drums were beat to drown out the screams of children being sacrificed.
"tempestuous wind Euroclydon": Euroclydon might be the east wind, but I couldn't find an exact match
"the copestone is on": 'Cope' refers to the highest course of masonry on a wall.
"Lazarus": A beggar, who lived on the doorstep of a rich man, 'Dives', below.
"Dives": Latin word meaning a rich man; used as a proper noun in the Bible story.
"Orion": the constellation.

Chapter 3:
"entry with old-fashioned wainscots": wainscots are wooden panels, paneling
"the New England hags"

"a boggy, soggy, squitchy picture truly"
OED: squitch:couch grass, a weed

"a Hyperborean winter scene": 'borean' would refer to the northern regions, 'hyper' is a Greek prefix meaning above or beyond.

"like another cursed Jonah": a reference to the Jonah who was swallowed by a whale
"specimens of skrimshander" From the dictionary: "scrimshaw, .... , 1. any of various carved or engraved articles made esp. by American whalers, usu. from whalebone or whale ivory"

"I sat down on a old wooden settle": a long seat with a back, a.k.a. a settee
"reported in the offing": the offing, 'part of sea distant from shore'.
"a sovereign cure for all colds and catarrhs whatsoever": catarrh, inflammation of a mucous membrane
"even with the arrantest topers": arrant, notoriously without moderation, toper, one who drinks to excess

"capering about most obstreperously":obstreperous, marked by unruly or aggressive noisyness

"and a chest like a coffer-dam": A coffer dam was a watertight enclosure usually made of two or more piles placed close together, with clay to seal it watertight. The water could be then pumped out, and a dry space provided. They were used to allow for the laying of piers or repairing of ships. Here, the analogy suggests that Bulkington was very muscular, like a body builder.

"now flying into a passion again at this unaccountable farrago of the landlord's": farrago:"a confused collection"
"I'll give ye a glim in a jiffy": glim may be from glimmer, but in this case, he means that he'll light Ishmael's way up
"Folding back the counterpane": Bed cover
"Going to his heavy grego, or wrapall, or dreadnaught"
dreadnought: a warm garment of thick cloth

Chapter 4:
"were in a horse-collar": part of the harness; made of leather and stuffed with straw.
"this is using Roger's best cutlery with a vengeance": Roger is the name of a cook in Chaucer's "Canterbury Tales"

Chapter 5:
Geographical:
"among the Green Mountains": A range extending from southern Quebec southwards through Vermont into west Massachusetts

Literary and Otherwise:
"and sea coopers,": a cooper is a person who works in copper
"with bosky beards": bosky may mean bushy
"seemed like the Andes' western slope"
"Ledyard, the great New England traveller,"
"and Mungo Park, the Scotch one": 1771-1806, explored in Africa

Chapter 6:
Geographical:
Broadway, Chestnut, Regent, Water streets; Apollo Green and Wapping:
Feegeeans=>Fiji, Tongatabooarrs=>Tongo islands?, Erromanggoans, Pannangians, Brighggians
"save in Salem,"
"drawing nigh the odorous Moluccas instead of the Puritanic sands."
see footnote in ch. 2 for Moluccas.

Literary or Otherwise:
"here comes another with a sou'-wester and a bombazine cloak."
A sou'wester is a long oilskin [oiled cloth, waterproof] coat, worn esp. at sea during heavy storms.
Bombazine cloth is either: a silk fabric in twill weave dyed black; or a twilled fabric with a silk warp and worsted filling.
A twill weave is one in which the filling threads pass over one and under several warp threads so as to give the appearance of diagonal lines.
Worsted is a smooth compact yarn from long wool fibers used esp. for firm, napless fabrics, carpets, or knitting.
A nap is a hairy or downy surface.

"this once scraggy scoria of a country?" Wasteland; scoria comes from a Greek word meaning extrement.
"Can Herr Alexander perform a feat like that?"

Chapter 7:
Geographical:
"Near the Isle of Desolation, off Patagonia": I. Desolation is at the western end of the Strait of Magellan

"As well might those tablets stand in Elephanta as here": Elephanta is a island west of India in the Bombay harbor.

"more secrets than the Goodwin Sands" The latter are shoals in the Strait of Dover, off of the SE coast of England.

Chapter 8:
"the spring verdure peeping forth": verdure can mean freshness or vigor.
"his great pilot cloth jacket"
"and overshoes were one by one removed": overshoes arewaterproof outer shoes worn over the regular shoes
"hansome pair of red worsted man-ropes":For a definition of 'worsted', see ch. 6, 'bombazine cloak'
"impregnable in his little Quebec"
"a lofty Ehrenbreitstein": a fortress in Coblenz, West Germany, built in the 12th century [Random House Unabridged Dictionary, 2nd ed.]
"Between the arble cenotaphs on either hand":Cenotaphs are memorial tablets for people buried elsewhere.
"Serenest azure is at hand": Azure can refer to a clear, cloudless sky.

Chapter 9:
"does Jonah's deep sealine sound!": a sea line is a long line used for fishing.
"what a pregnant lesson to us": deeply signifagant
"that canticle in the fish's belly!": a canticle: one of the nonmetrical hymns or chants, .... , used in church services. [Random House]
"this son of Amittai"
"Jonah still further flouts at God": flout: to treat with contemptuous disregard. [Webster's]
"the wharves of Joppa"=Jaffa, is a former city west of Israel, but now is the sothern part of Tel Aviv
"bound for Tarshis"=Cadiz, a province in southwest Spain
"skulking from his God": moving in a stealthly or furtive manner [Webster's]
"not a hat-box, valise, or carpet-bag": a valise is a traveling bag; a carpet-bag is one made out of carpet.
"but whose cupidity exposes it": avarice, greed for money.
"the Roman race-horse"
"startled from his lethargy by that direful cry": lethargy, abnormal drowsiness.
"a panther billow leaping over the bulwarks"

Chapter 10:
"and with a jack-knife": 'a large, strong clasp knife for the pocket' [Webster's]
"at the storm from the casement": a window with a particular kind of sash.
"like the dyspeptic old woman":dispepsia is related to indigestion.
"us silent, solitary twain": twain can mean a couple or pair. [Webster's]
"took out his enormous tobacco wallet": 'wallet, .... :a bag for carring misc. articles while travelling' [Webster's]