Other mistake: At the end of the film when they arrive in NYC looking for the library, we know that they survived because they are inside with a roaring fire burning. But where is the smoke up above, as Jack Hall approaches? There must be a chimney, or else they would have all died of asphyxiation.
Visible crew/equipment: When Jack is in the library towards the end of the movie, he looks in a room and then the shot goes back to facing him. If you look very carefully, in the back of the hall you can see a person walk by. He is very hard to see. (01:49:05)
Character mistake: When Jack arrives in New York he's right next to the Statue of Liberty. However when he reaches the library he comes from the East River and walks west. That is a pretty big detour around the southeastern corner of Manhattan, instead of taking the direct route. (01:47:00 - 01:48:20)
Factual error: Given that the entire premise of the movie revolves around the melting of the ice caps and the disruption this causes, including a rise in sea-levels, and that at then end of the movie most of the Northern Hemisphere outside the tropics is covered by an enormously enlarged ice cap the sea-level should have lowered significantly enough for the shape of the land masses to appear different from space.
Factual error: At the end of the film a wing of Black Hawk helicopters are dispatched to NYC to evacuate survivors. The Black Hawk does not have anywhere near the fuel capacity for such a trip. And at its cruising speed, it would take a day to get there anyway.
Plot hole: Dennis Quaid and his companion seem to have no problems staying warm in just a tent while preparing to sleep for the night; they are actually shown with removed layers of clothing while in the tent. Yet the survivors in the library are covered from head to toe in clothing and blankets.
Other mistake: At the end when Jack walks into the room where everyone is and shines his flashlight around, you see the nerd and the rich kid with the librarian in the background. Then you see a girl next to Sam's girlfriend. Where did she come from?
Factual error: When the big wave comes, it's hitting New York harbor and the Statue of Liberty from the west. Possible I guess but unlikely due to the fact that the harbor just starts there; the west side of the harbor isn't the ocean side, it's New Jersey. Later, the people are standing in front of the library, which faces east and the wave is coming right at them. Then they show an overhead shot of the water overtaking the city and its coming from the south.
Factual error: When some people are burning books in the library, one man is adamantly protecting a Gutenberg Bible. Considering how rare and valuable Gutenberg Bibles are, it would not have been on the shelf or even readily accessible. Likely it would be locked in a safe or at least a showcase. Considering the shortage of time to collect fuel and the plethora of books available, I doubt they would break into a locked container to get another bit of fuel.
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.