Pretty well, actually. The costumes, props, sets, everything was pretty meticulously researched and they do a very good job of avoiding anachronisms or introducing stuff that's just flat out fiction. About the only thing that really made me raise my eyebrows was the fact that the Acheron was supposedly a "44 gun privateer, Boston-built". That means it would have construction very similar to the USS Constitution, which needed a crew of about 450, including a complement of Marines. That's obscenely huge for a truly independent privateer, unless the term privateer was supposed to be a colloquialism for an actual French warship operating independently in foreign waters.

The clothes, the battle scenes, and how the men conducted themselves on the ship day-to-day is spot on. They did a great job showing how cramped, wet, dirty, and smelly life aboard a sloop or sixth-rate frigate would be. The little things, like a servant for every officer during the dinner scene in Aubrey's cabin, and how messy and disgusting the surgery scenes in the wardroom were during the battles were excellent. Showing the separate room for the lantern adjacent to the magazine, and the powder room sailors going barefoot were good too. The Rose is a replica of the HMS Rose of the era, so the construction of the ship is about as accurate as we'll get without using the Victory to film scenes, or going back in time.

People like to complain about little technicalities, like the amount of live-fire gunnery practice they did halfway through the movie, in the middle of nowhere, with no chance of re-supply. That's a needless and expensive expenditure of shot and powder; the vast majority of gun exercises would have been "dry runs", where everybody went through the motions but didn't actually touch off any rounds. However, it's a movie and they needed to fold that "getting better" montage in somewhere sensible, so I get it.

TL;DR- A few minor, minor quibbles, but the movie is pretty spot.