Factual error: It is not feasible for a flood to stop the flow of warm air for the northern hemisphere and make it as cold as it did in the movie. The air moves far too fast for anything to stop the flow of warm air in the northern hemisphere.
Continuity mistake: When Jack arrives in New York he's right next to the Statue of Liberty. When the camera pans abowe the Statue of Liberty, you can see that front of the Statue is in light, and it's back in shadow. In the next shot front of the Statue is in shadow, and back in light. (01:42:35)
Continuity mistake: When Jack and the other bloke are standing and ask where the library is, they take off their skis and sled, and run a few metres and look over a sand dune. The camera zooms out a fair bit, but the sled has disappeared. (01:43:05)
Character mistake: The news reporter says that people are fleeing in the wake of the storm, meaning after the storm, not before the storm, which is what she should have said.
Other mistake: When the supercooled air is shown coming down, it makes all the windows in the skyscrapers explode. The library room they were in had 2 windows. These also should have exploded and the cold air should have killed them.
Other mistake: When his dad arrives at the library, the opening is larger and the raft with the food is gone. Had they gone out to get it after the storm passed, the doors would not have been frozen shut so neatly.
Suggested correction: Jack and Jason entered the library through a broken window in the large room they were initially gathered in shortly after the tidal wave. The raft with the food on it probably froze during the big freeze, so they never left the room after the storm passed.
Other mistake: At the beginning of the film, where Jack falls into the crevice, he's got nothing in his hands. In the next shot, you see he's clinging to the side of the crevice with an ice pick that has mysteriously appeared in his right hand.
Suggested correction: He probably had it hanging from a belt or something seeing as where he is he probably has a tool belt of things just in case something like that happens. He probably just grabbed it from the side you couldn't see.
There was nothing resembling an ice pick hanging from his belt before he fell.