K-19 may be historically inaccurate, but show me a military movie that isn't. This film is way more true to life than the idiotic fantasy that was U-571, in which Americans won the second world war by capturing a cipher machine (FYI, it was a British crew who captured the machine and anyway the Brits already had one, reverse-engineered by Polish intelligence and given to them in one of the more stunningly generous acts of wartime cooperation).
The important thing is not so much how doggedly authentic the story is. After all, Wolfgang Petersen's classic 'Das Boot', surely the ultimate sub movie ever in its original miniseries form, is fictional. What matters is the quality of the story, and the story told here in K-19 is profoundly touching. Harrison Ford seems really engaged for the first time in a long time, Liam Neeson is properly cast for a change as a slightly ambiguous figure (instead of just as a nice guy) and Peter Sarsgaard is heartbreaking as the head of the team that attempts to repair K-19's reactor.
Kathryn Bigelow's films have veered between genuinely eerie (Near Dark, The Loveless), silly (Point Break, Blue Steel) and romantic but a bit daft (Strange Days). For my money, this is the first movie she's made that her fans don't have to apologise for. So who cares that the crew all have silly Russian accents? Like you'd prefer that Harrison Ford sounded American and Liam Neeson sounded like he was from Ballymena? The sadness and grimness of life in the USSR have not generally been paid attention to by US filmmakers, who for the most part portrayed Soviets as cannon fodder, but this is a brave effort and a gripping and affecting movie.