How much I forgive a film for historic inaccuracy rather depends on what is being depicted and why.
Example: Supposedly Spartacus was killed in battle, not crucified, but no-one really knows for sure, so I was perfectly happy to grant Kubrick artistic licence for his 1960 film.
The Great Escape has plenty of factual liberties, but they are ones I don't take issue with as they serve the story better from a cinematic perspective (for example, the escaped prisoners that were murdered were not all murdered together). And yes, there were no American prisoners in that camp, but having Steve McQueen's character in the mix too adds to the entertainment value, and I don't see a problem with that.
Elsewhere, I get very annoyed with certain kinds of nit-picking. John Boorman's Excalibur is based in fantasy, therefore who cares whether they include anachronistic plate armour? I also have little sympathy for the bores who pointed out that Dunkirk contained certain types of military craft there were only used in 1941, not 1940.
On the other hand, we know damn well that the Americans weren't even in the war in 1940, when the Enigma decoding machine was captured. So the film U-571 was rightly laughed out of court.
Against that, I have to confess that as a cineaste, I mark films on their cinematic merits first and foremost, and their historic accuracy second. To that end, regarding the films on this list:
1. JFK - I love this film. Yes, it is bonkers from a historical perspective, but as a piece of cinema it is outstanding, with superb performances, innovative direction, and a first-rate screenplay that delivers a ton of exposition with immense skill.
Regardless of how much the film is barking up the wrong tree historically, I'm pretty sure there was something rotten in Denmark with the Kennedy assassination, so I'm perfectly happy for Oliver Grindstone (as my father called him) to speculate. Speaking of my father, I recall leaving the cinema after going to see this with him, and asking him how he was involved in the Kennedy conspiracy. After all, Stone had implicated pretty much everyone who was alive in 1963.
Did it inspire a generation of conspiracy theory nutters? I'm not sure I buy that. I think the darker corners of the internet bear a much heavier burden on that score.
2. Apocalypto - Guilty as charged from your point of view, but I still enjoyed this is as a deranged and bloody adventure romp.
3. The Patriot - A much lesser film cinematically, and everything you claim is correct. As a Brit, I am bound to be irritated by it (as I am by the aforementioned U-571, amongst others).
4. Braveheart - A well put together film which plays up the myth of Wallace, but not at the expense of realism (the bloody battle scenes are very well done). However, it is historically dubious, and undoubtedly stirred a lot of nasty nationalistic feeling in Scotland, so I can't argue with that. Also the liaison with Isabella is laughable, but to Gibson's credit apparently it was put in at the studio's insistence, not his.
5. Pearl Harbor - Michael Bay films are an anathema to me, and this one was no exception. So go ahead and duff it up as much as you like from a history perspective.
An interesting read. Thank you.