I enjoyed it - historical inaccuracies and all (nod to Garyq), but that's why they say "based on". I'm tempted to track down the actual story of what happened simply because so many things went wrong. Granted, it took place in the early 1960s, but the idea of sending a nuclear-powered submarine out that was basically held together by spit and bailing wire (and unauthorized prayer) is pretty irresponsible, even if you weren't fully cognizant of the dangers of radiation exposure. Brr.
One of the cool things about it was finding people of my father's profession cast as the heroes of the piece. Dad was a pipefitter for the Atomic Energy Commission in Idaho, and then for the Puget Sound Naval Shipyard when we moved out here to Bremerton. It was doubly interesting because he did a lot of his work on nuclear submarines/ships - until he'd logged enough exposure that he had to transfer to working on the power plant.
It was the pipefitting and welding crew that saved the ship in the film, at the cost of their lives, when one of the reactor cores lost coolant function and began to overheat. They managed to figure out a way to re-route the fresh water supply (coolant==distilled water) into the core, but it involved going in and working in the unshielded reactor area. So the six men who made the repairs were horribly irradiated, and the entire submarine was contaminated to a greater or lesser degree. But it kept the core from melting down and setting off a chain reaction, or setting off any of the warheads they were carrying.
I've been on a Trident submarine, and I plan to try and get down to tour the Russian sub that's at the waterfront (when I'm a little more mobile - those things are cramped) - the film did a pretty good job of portraying how little room there is on board. It's probably worth seeing if you like this sort of thing at all - the consensus of the group that I went with was positive.
Oh, yeah. The other thing about my dad's career: he spent the first half of it lagging asbestos insulation onto pipes and the second half of his career removing it. Don't try and tell me the universe isn't perverse.