Mel Gibson's movies like Apocalypto and Braveheart. While it may seem like having a movie in Maya adds an extra layer of authenticity to the films, I think it may give people the impression that films like Apocalypto are historically accurate.
Focusing on Apocalypto specifically, the movie has a pretty inaccurate portrayal of Mayans. The opening hunting scene of the movie betrays a group of Mayans or another Mesoamerican people hunting a tapir, which contradicts the Ancient Mayan lifestyle and most Mesoamerican cultures at that time which were largely agriculture. The appearance of the tribe itself portrays them more as some isolated neolithic Amazonian tribe rather than the intricate society where women dressed more conservatively. That's not even the worst inaccuracy of the movie.
In my opinion at least, movies that are based on history should strive to be as accurate as possible (ala Dances with Wolves) or just flat out throw away everything and create a fantasy movie (ala 10,000 BC) but when you try to be both, 9-times-out-of-10 you just end up with something awkward to anyone aware of history.
Maybe it's just me, I'm a very nitpicky person when it comes to movies, but am I wrong for wanting historical films to be at least semi-historically accurate?
EDIT: Removed the mention of the Passion of the Christ as looking it up it's a biblical drama, I just ignorantly assumed it tried to be historically accurate (as accurate as a biblical story can be).