Factual error: In the beginning, James is collecting insects but it is cold enough for snow. Insects don't stay exposed to the cold like that.
Plot hole: How was Cole supposed to get on a plane without having any identification documents?
Revealing mistake: The paint in the "we did it" lettering in the roaring bear scene runs "downwards," according to the camera position, not according to the vertical of the shot buildings. (01:51:15)
Suggested correction: While yes there are slight angles involved, considering this was most likely a physical prop on-set, the direction of the camera tilt wouldn't be a factor. The direction the paint runs in doesn't seem wildly inconsistent with what would happen when painting something like that.
Continuity mistake: Before Cole returns to his own time for first time, he has several wounds on his head and face which disappear when he talks with the bosses.
Factual error: In the madhouse scene where Brad Pitt is jumping on beds and ripping up pillows, feathers are strewn about. Feather pillows are never used in secure facilities, for sanitary and allergic reasons.
Suggested correction: Pretty easy to do pre-9/11.
Rlvlk
I flew for most of my business career. Starting in the middle 80s, you had to have proper identification to get a boarding pass which let you on the airplane. each flight had a manifest with names and addresses of the passengers. Even with the post 9/11 changes, I think the current procedures are pretty sloppy compared to the 90s.
sexxypeety