Continuity mistake: At the end when Sarchie is hugging his wife, in one shot the bandage on his arm has unravelled. In the next, it is neatly wrapped.
Continuity mistake: When we first see the male volcano, he is an entire island with trees and forests. After many years have passed and sinks into the ocean, it can be seen the trees and forests have now gone. However, after he spews out of the ocean and is together with the female volcano, the male volcano suddenly has trees and forests around him again.
Factual error: While Evans and Eve are still in Grand Central they overhear an announcement which states "According to Port Authority policy This station will be closing for the evening." Grand Central is not part of the NY/NJ Port Authority. Also Grand Central is a terminal, not a station, as trains do not pass through Grand Central, they enter and turn around.
Factual error: During the Hungnam evacuation scene in December 1950, a U.S. Army Captain is using a radio handset. The model he uses is the H-250, which was introduced in 1987, over 30 years after the Korean War.
Continuity mistake: Jay is mopping the floor after promising on the phone to his dad that he'll bring his non-existent fiancee to the wedding. He tries to talk one of the nurses into joining him. While doing so, he stands before her leaning on his mop with his left hand on top, which switches to the right hand between shots. (00:06:40)
Character mistake: Mitch states that he is Pisces then goes on to state that his birthday is 25th of March. The Pisces period goes from 19th February to 20th of March. Mitch would actually be Aries. (00:35:00 - 00:37:00)
Continuity mistake: Vincent and Oliver are eating ice cream, Vincent's ice cream cone repeatedly changes levels of ice cream left in his ice cream cone as he eats it. (00:48:00)
Continuity mistake: When the crocodile catches the man he bites his right foot off. 5 seconds later as he falls into the water his foot is back. (01:21:05)
Character mistake: When Jesperson imagines himself as a Mountie his uniform is completely wrong and is not even the right colour. As it was his ambition to join the force and he has photos of RCMP officers in his cab, it seems unlikely that he would imagine himself in a completely incorrect uniform.
Suggested correction: It's not a character mistake, for the reasons stated; it's a clear factual error from the filmmakers.
It's a character mistake since it's his imagination and, as you stated, it's not something the character would get wrong.
Continuity mistake: While father and son are eating beignets, the passers-by behind them are not continuous between shots.
Other mistake: It is stated by the caption ("The far East; 3 years later") that the events of most of the movie take place 3 years after the prologue. Thus, both Nicolas Cage and Hayden Christensen have made it to China and learned flawless Chinese (there's no language barrier whatsoever and they understand each other perfectly at all times) in less time than that, while being on crack and on other considerable hardships, too.
Other mistake: After the longest introduction ever, a text crawl (in English in the original version too) details the event leading to the titular fight club. It says that the city fell "A PART" and the institution "IS COLLAPSED." Also, it warns us; "cannibalistic zombies are malformed." (00:59:30)
Character mistake: At the end of the movie, when Jaggu is listening to the sounds recorded by PK, the audio contains the question which she asked, "Tumhare planet pe sab aise hi hote, bade kan wale?" but does not contain the answer which PK gave, even though he was sitting right there. This seems to suggest that PK did not exist in the real world.
Continuity mistake: Felix pushes the fire alarm button and exits the building. As his buddy Danny reaches him, it's obvious that multiple takes of the scene have been made, since some extras that were meters ahead of him are just passing him by at the very first cut. (00:04:30)
Revealing mistake: JR is in the weapon container of the crazy dealer, who passes him some of his goods. JR ends up holding in his right arm a MP5K and an M4A1, which combined are about 5 kilos, but then he passes him an M60 Machine Gun, which weighs over 10 kilos and that the relatively diminutive protagonist just handles throughout the scene gripping it with his left hand and making no effort whatsoever. (00:25:20)
Factual error: When the guy is talking to him on the phone and the Russian smashes it on the floor, the phone smashes and the battery comes out but the guy other end can still hear him. (01:04:00)
Continuity mistake: The big bad boss is saying big bad boss things to the protagonist as he rolls up the sleeve. Salma Hayek tells him to shut up and just do it; in that camera angle, the actor (or his body double) has his arms down his side doing nothing, while when Hiroyuki Watanabe is fully in frame he is moving. (01:10:45)
Continuity mistake: Before Jesse's plate is placed on the table, the salt and pepper shakers are about a width apart. They are almost touching for a while, then back to being spaced apart. (00:10:20 - 00:11:00)
Continuity mistake: Stretch takes the licence plate off the limo just before it's stolen. When he's clinging onto the bumper as it's being towed, the plate is back on.
Continuity mistake: Kevin Shepherd pulls over in front of her fiancee's dad. It's still a wide angle, but you can see distinctly both her and his left arm stretched forward; she is looking at her engagement ring, he has his hand on the steering wheel. Before the camera cuts away though, he lowers his arm; it is not acknowledged in the new shot, where both have still their left arm forward. (00:03:35)