Factual error: Roland enters the train to go to the war, in 1914, with "Spanish Flu", but that was the (wrong) name given to the 1918 flu pandemic, which lasted from spring 1918 through spring or early summer 1919.
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.
Continuity mistake: Judge Pendergast calls the daughter of his therapist, who reacts with typical New York aplomb. During the scene, the same extras continue to walk back and forth with no logic, sometimes coming twice from the same direction, even. Most egregious example the blonde with a ponytail and sunglasses on top of her head. She is behind Jennifer Aniston in the opening shot and appears at least 4 times (possibly more but there's another blonde too -unless it's the same one who occasionally removed the glasses) and walks away from Aniston and Forte two times in a row. (00:17:40)
Factual error: When the Germans come to the town a tank rolls through the picture. The first shot shows the tracks, then the whole tank is shown and one can see the tracks again. The turret suggests a Panzer III (which would be accurate for the time). It appears however that the tank is a modified Russian T34 or T55 or something as the road wheels are too big for a Panzer III. (00:13:00)
Other mistake: Elizabeth Banks' husband says it's 4 in the morning but there's daylight coming through the window.
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.
Continuity mistake: As the jeep with the killer goes over the cliff and smashes face down you can see nobody is in the jeep as it disintegrates the front part. (01:14:00)
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: When the guy is protecting his home and clearing the window with his shotgun you can see him breaking the glass on the bottom left window pane. In next shot it has the piece there again. (01:43:55)
Continuity mistake: Treat Williams is drinking a brown liquid from a glass (scotch?) while accusing Gina Carano of having something to do with his son's disappearance. Shortly afterwards, the liquid is a different color and the glass is much more full. (00:41:40 - 00:42:40)
Continuity mistake: In the "Another Brick in the Wall Part III" section of the show, look at the missing section of the wall on the right hand side. The bottom bricks of that section change from being filled in to being empty depending on the shot. (01:02:40 - 01:04:00)
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)
Factual error: Newgate makes a reference to Mickey Finn's name being the same as that of a Chicago bartender who used to drug his patrons with knockout drops. However, the film is set in 1899, but the real Mickey Finn wasn't caught until 1903.
Continuity mistake: When the kids are looking at the Stonehenge-type structures, the younger boy calls for everybody to come and see the hidden message. From the shot in front of the boy you can tell from his body position he's sitting up, however in the next shot from overhead, the boy is now lying down on the rock.
Factual error: The alien drops the video camera out of the UFO from outer space and it falls to earth landing on the ground. This very far drop would certainly have busted it to pieces, if not ignited it on reentry, but when the guy picks it up off the ground, it appears only the screen is cracked.
Revealing mistake: Tortured by the demonic voices in his head, Michael King goes into a self-mutilating frenzy with a kitchen knife, except that he squeezes the handle of the bleeding-knife prop a bit too hard and it squirts fake blood horizontally across his chest.
Continuity mistake: At the end of the film we see stuff being crossed out in a notebook. The lines that are drawn through the words keep changing from being perfectly straight to being at an angle.
Other mistake: During the driving scene in the woods with the Bronco, at least two shots are reused twice.
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.
Other mistake: In the flashback to Richard's childhood, when he looks from the door at his dad randomly shagging a party guest, the door appears open wider in the POV than it is in the other shots, where the opening barely fits his head. Besides, with the head in that position, he wouldn't see the door handle as shown. (00:02:00)