Thankfully, the connection with Moby Dick is a lot feebler; In the Heart of the Sea is an adaptation of Nathaniel Philbrick's excellent novel, based on a true event - the sinking of the ship Essex by a whale - which inspired Melville's classic.
The movie commits three major narrative blunders.
First, the usual, overwrought framing device, with survivor Nickerson (Gleeson) recounting the disaster and the crew's following ordeal to Melville (Whishaw). Not only the meeting never happened (Nickerson wrote down his memoirs for a minor writer, who never used them); the movie keeps cutting to Nickerson and Melville, dissipating any tension and momentum the survivors' struggle may gather. Imagine a version of Cast Away where, every ten minutes on the island, we cut to a scene of Tom Hanks interviewed by a journalist after returning home.
Second problem: characters. The most interesting element of Philbrick's novel is how Captain Pollard (here played by Benjamin Walker), decent but irresolute, is the more sympathetic character, while first mate Chase (Chris Hemsworth), harsh but determined, is the more charismatic.
As is typical of blockbusters, the movie chooses a single protagonist (Chase/Hemsworth) and whitewashes him to an absurd extent. He was supposed to become Captain, but was robbed of his rank! (He wasn't - Pollard was the Essex' previous first mate). Chase was popular among the crew! (He wasn't, many feared and disliked him). And so on. Even Walker's supercilious Pollard eventually bows to Thor's superiority. A pity, because Chase would have been FAR more intriguing with his darker edges.
Third problem: Howard's penchant for melodrama rears its ugly head. Director and scriptwriters felt the need to spice up this compelling story with inventions (like the whale chasing the crew for weeks after the attack, or a one-harmed sailor warning them about the beast), while omitting details with the flavor of real life (a sailor setting an island on fire out of sheer idiocy, a hunting party aborted after a terrible roar in a jaguar-infested jungle) and crucial mistakes: Pollard wanted to sail to the Society Islands after the disaster, which would probably have saved many lives, but was irresolute enough to be persuaded by his officers to head to South America instead.
The result is watchable, but lightweight - the one adjective one would NEVER use for the literary classic the movie so portentously tries to evoke.