“The Finest Hours” tells the story of a little-known yet fairly incredible 1950s rescue mission, in which a four-man band of Coast Guard troops went above and beyond the call of duty, steering out into impossible sea conditions in the dead of night to reach a crippled oil tanker. So perhaps the worst one could say about Craig Gillespie’s film is that, rather than their finest hours, the whole cast and crew all put in a solid shift at the office making the movie, producing a perfectly entertaining, sometimes quite well-crafted disaster drama that nonetheless retreats from the memory almost as soon as the credits roll. The disappointing returns for Ron Howard’s recent seafaring saga “In the Heart of the Sea” should give the producers pause, but the film certainly offers enough to provide a modest-sized audience with some respite from the horrors of the January multiplex.

Like “The Perfect Storm,” the film takes place off the coast of Massachusetts during a particularly vicious nor’easter, yet here the focus is divided evenly between a commercial ship in distress and the rescue party heading straight for it. The former is the Pendleton, an oil tanker that split in half under rough waters in winter of 1952, leaving the fore section at the bottom of the sea, and the surviving sailors in its aft section adrift with no radio or commanding officers. The latter is the humble Coast Guard boat dispatched to find the Pendleton, a task that goes from difficult to effectively impossible when night falls and the boat’s compass breaks.

Once it gets to the moment of truth, “The Finest Hours” is a fully respectable nautical nailbiter. Unfortunately, it does take its sweet time getting its sea legs, opening up with the first-date-to-engagement courtship of young Coast Guard sailor Bernie Webber (a square-jawed, taciturn Chris Pine) and telephone operator Miriam (Holliday Grainger). Director Gillespie is a sure hand with sweet small-town repartee (see “Lars and the Real Girl”), and the film does yeoman’s work to make Miriam into more than just a thankless girlfriend character, but it’s hard to get too invested in this long prelude, knowing their romance is only being set up to ratchet up the emotional stakes once one of them gets lost at sea.

Gillespie is clearly more comfortable off land, and as the storm rolls in, the film provides a dose of high-seas drama on the ill-fated oil tanker, as the boat’s chief engineer, Ray Sybert (Casey Affleck), takes de facto command of the vessel’s survivors, not all of whom are thrilled about suddenly taking orders from a scrawny, socially awkward bookworm. The boat is filled with stock types, from the He-Man Scotsman (Graham McTavish) to the jolly cook (Abraham Benrubi) and insubordinate bad apple (Michael Raymond James), but Gillespie’s excitable camerawork — swooping up and down through the layers of the ship, following the crew as they shout messages through the corridors in an elaborate game of telephone — helps bring the ship to life. (Curiously, Boston native Affleck is one of the few actors here to eschew a broad New England accent, and perhaps uncoincidentally he registers as the cast standout.)

After a good deal of hemming and hawing back on shore, the local commanding officer (Eric Bana, sporting a patchy Southern drawl and filling out an underwritten antagonist role) decides to send Bernie out to search for survivors in a 36-foot-boat, despite the locals’ assurance that a vessel of that size would never make it past the sandbar in current conditions. Bernie takes volunteers Richard (Ben Foster) and Andy (Kyle Gallner), as well as a woefully unprepared seaman (John Magaro) who just happened to be passing at the outpost for the night.

For the earlygoing at least, the film hits its audience with a barrage of nautical jargon and trusts them to fill in the details, and that decision pays off most fully in the harrowing, believable sequence in which Bernie and Co. climb giant wave after giant wave just to make it out to the open ocean, their tiny boat frequently submerged and rolled end-over-end.

Once Bernie gets out to sea, Gillespie crosscuts among his attempts to navigate choppy, snowy waters sans compass, Ray’s increasingly desperate measures to maximize the oil tanker’s chances, and Miriam, striding bravely into Coast Guard offices and getting her car stuck in a snowbank. Needless to say, the latter is the least engaging of the three threads, and Gillespie spends a bit too much time while ashore establishing a redemption narrative for Bernie, who once failed to rescue some locals in similar conditions. Like so many disaster films, “The Finest Hours” fails to grasp that simple survival is all the motivation these characters need, and that it’s actually far nobler to show these Guardsmen heading into probable death simply because it’s their job than because of any specific personal demons.

In any case, the rescue scenes at sea are tautly edited and well staged, more concerned with emphasizing the cold, wet, disorienting conditions than awing with CGI setpieces. Composer Carter Burwell, working in a far more classic idiom here than his recent scores for “Carol” and “Anomalisa,” helps craft a very old-school mood, and d.p. Javier Aguirresarobe does typically strong work. However, save for a few reliably impressive shots of massive waves, the dim 3D adds very little, and there’s something almost perverse about applying it to so many scenes where characters are dealing with zero-visibility conditions.