Accidental Innuendo: It was noted even at the time it was published that some of the symbolism and word choices were a bit suggestive, which Melville apparently didn't notice until later pointed out to him.
Fittingly, his nemesis. Moby Dick — normal, aggressive, oddly colored sperm whale, or supernatural Animalistic Abomination in the shape of one?
Due to the sperm whale being very aggressive by nature and as a result known to attack ships without being provoked the question of whether or not Moby Dick defending himself or attacking ships for no reason is left unanswered. As is the question if he has any idea who Ahab even is.
Queequeg: Cap'n, ee see him small dark spot on water there? Ee see him? Well, s'pose him one whale eye! Well, den...(throws harpoon and hits the oil spot with a dead bulls-eye) Dat whale dead.
Ahab's death in the 1956 film:
Ahab: (strapped to Moby Dick and stabbing him repeatedly with a harpoon) "From Hell's heart, I stab at thee! For hate's sake I spit my last breath at thee! THOU DAMNED WHALE!"
Crazy Awesome: Ahab. It is because of his insane obsession with Moby Dick that he created charts accurately mapping the annual movements of the whales, allowing them to follow the herd, kill as they go and fill their hold in record time. His insanity also wins over his crew and makes them all (save for Starbuck) extremely loyal and invested in the hunt for Moby Dick.
To modern readers, the three harpooneers can come across as caricatures of Africans (Daggoo), Native Americans (Tashtego) and Polynesians (Queequeg), respectively. However, Melville makes them all sympathetic characters and Ishmael frequently talks about how they're Not So Different from white men. In fact, he deliberately created them to defy stereotypes, with Tashtego being gloomy and fatalistic while Queequeg is cheerful and down-to-earth.
"Better to sleep next to a sober cannibal than a drunken Christian."
Through most of Moby-Dick, the sperm whale was a monster, the legendary leviathan to be hunted down and killed for its oil and spermaceti. Melville admonished people not to burn sperm-candles or lamp oil recklessly, not because he wished to spare the whales' lives, but because so many human sailors died every year on whaling expeditions. In the modern world, just about every species of whale is endangered, and whaling was one of the main reasons for their dangerously low numbers in the wild; "save the whales" is a rallying cry more people support than oppose and thus people are more likely now to cheer on Moby defending himself. Yet at the time the story was written, whale populations were much larger, and nothing was known of whalesong or other such indicators of cetacean intelligence.
Harsher in Hindsight: Ishmael doesn't believe whaling is a threat to the whale as a species since unlike shooting buffaloo, whaling was (at the time) dangerous, time consuming, and known for voyages coming back empty handed. The book was published in 1851, the first practical harpoon cannon was invented in 1863. He also used the elephant surviving thousands of years of hunting as an example.
The most egregious examples of this appear in the chapter called "A Squeeze of the Hand", which is about the delights of immersing one's hands in sperm whale oil and kneading it to keep it liquid.
"Come; let us squeeze hands all round; nay, let us all squeeze ourselves into each other; let us squeeze ourselves universally into the very milk and sperm of kindness."
Far, far more egregious are the detailed descriptions of Ishmael's and Queequeg's sleeping arrangements:
Upon waking next morning about daylight, I found Queequeg's arm thrown over me in the most loving and affectionate manner. You had almost thought I had been his wife.
Captain Ahab and Mr. Starbuck definitely have something going on, at least one-sidedly (on the part of Ahab). At one point, Ahab quite literally tells Starbuck he would prefer to gaze into his eyes than see the face of God (which sounds silly nowadays, but would have carried a huge amount of weight back when the book took place, as religion was essentially the be-all-end-all of most people's lives back then).
Starbuck, of late Ive felt strangely moved to thee; ever since that hour we both sawthou knowst what, in one anothers eyes".
Mainstream Obscurity: Moby was a whale. Everyone knows that. Not so many people have read the books.
Moral Event Horizon: Ahab dances along the edge of it for most of the story, but finally crosses it when, rather than help the Captain of the Rachel find his lost crewmembers - among them his own son - he chooses instead to pick up the trail of Moby-Dick before it goes cold. In true Greek Tragedy fashion, everything goes downhill fast after he makes this choice.
Nightmare Fuel: Moby Dick himself. As stated many times across the Moby Dick pages on this very wiki, being a sperm whale he is naturally aggressive and will attack ships without provocation. He has sent who knows how many to their deaths and is treated by whalers as if he is some sort of demon, which probably makes him worse to those whose captains drag them after him. Moby Dick attacking without provocation: scary. Actually giving him a reason to attack you: scarier.
Rooting for the Empire: In modern culture most people will be cheering Moby on as he kills everyone, no matter how sympathetic adaptations try to make the crew. This is because in modern times with the high intelligence of whales being well known, most people don't see Moby Dick as a remorseless monster but as an innocent victim just defending himself. However, people with this view fail to realize that sperm whales are very aggressive by nature and have been known to attack ships without being provoked.
Whether or not you approve of whaling, it is more controversial today than it was when Moby Dick was published, what with environmentalism and concern for endangered species.
The story does explicitly discuss whether Man could hunt whales to extinction. Already their numbers are diminishing, but the author's opinion is that they'll avoid Man by swimming North to the icy oceans, and so will always be able to evade extermination. It's an opinion based on flawed biology; given better science it could have gone the other way. Even so, Melville gives consideration to it.
The narration offers a defense of whaling by mentioning the benefits to humanity whale oil has had and also talks about how the whaling vessels allowed the liberation of the South American countries from Spanish imperial power, led to the successful colonisation of Australia, opened up the Polynesian islands to Europeans and forecasts whalers as being the cause for Japan to end its isolationism. To modern readers this can easily be read as the whaling industry being a figure to blame not only for the decline of cetaceans but also the suppression and decimation of tribal cultures and the resulting tragedy from Japan's rapid modernisation.
This work in particular took several decades to attain the critical status it enjoys today. Melville was previously a successful author of travel books that are forgotten today; after the failure of Moby Dick, his career declined. As a literary critic noted, he's probably the only writer in history to be ruined by his one masterpiece.
In the Reader's Digest: World's Best Reading edition, Thomas Fleming states in the Afterword that critics scoffed at the idea of someone going as far as Ahab did, and everyone around simply obeying...until they lived through World War I.