Historic inaccuracies don't bother me. Usually. Because often the inaccuracy is deliberate, x is replaced w/z to make a story a better story. Usually its about the plot, or a gameplay mechanic, and the 'history' in the game is meant to be nothing more than a setting for the game/plot/action/scenes to take place in.
When they *do* bother me is:
when i suspect the developer didn't realize what they've done is inaccurate (then its just embarrassing).
when its so conspicuous that it causes me to lose immersion.
when its for the purpose of converting me to some viewpoint, i.e. moralistic preaching.
When its logically inconsistent w/something else in the game.
When the goal of the game is to not only be entertaining, but also to be educational. If one of your goals is to educate, then take some effort to get your facts correct. If ya just want to entertain, however, then have at it!
When its not obvious that its inaccurate, but it would bad if people walked away thinking it *was* accurate, i.e. spreading misinformation on some serious subject or other.
When its a genre-shift. Example - game starts out in early 1900's england, and you just start to become immersed, when suddenly halfway through now there are aliens (shift from historic to sci-fi). -> I started playing the game because I was in the mood for X, and i started off getting X, but suddenly i'm getting Z, something I wasn't in the mood for. If I was in the mood for Z, I would have played a game that was Z through and through. If I know about the genre shift before hand, that's fine, or if its really well pulled off, but it rarely is. (not just games, look at the latest indiana jones movie. Not that these movies have a history of accuracy or anything. But the latest movie had this genre shift type thing I mention here. Not a bad movie, but I didn't go to the theatre and pick the indiana jones movie because i was in the mood for sci-fi. Felt like i ordered oranges and got apples. Doesn't matter how good the apples are, I wanted oranges).