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.
Other mistake: None of the men in the movie grow any facial hair at all, even the ones stuck in the library in New York.
Suggested correction: The storm only lasts a few days to a week at most, which isn't too much time for a guy to grow facial hair.
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)
Suggested correction: You never see anyone walk by. It's only him and his friend Jason. It's also very dark in the hallways so may have been a shadow.
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.
Suggested correction: Ice that accumulated on land doesn't change sea levels enough to make the continents appear different.
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)
Suggested correction: Easier to walk in an open area and have a short distance walking between buildings rather than walking through the city where the terrain may not be the best even with the snow/ice.
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.
Suggested correction: Jack and Jason are both extremely close to the heat source in the tent when they sleep at night (within a foot or less) and it's also possible the tent is rated for arctic survival, whereas the survivors in the library aren't always close to the only heat source (being the fireplace). Just because you are inside doesn't mean it's automatically warm. Just like in a house or a garage, even with proper insulation the temperature inside can be equal to the temperature outside.
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.
Suggested correction: We don't know where the helicopters originated from. We only see the head of the NOAA hop in one down in Mexico, and then we cut to the fleet over NYC. He also is wearing heavier clothing for winter conditions so it's possible they originated from elsewhere.
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.
Suggested correction: The water is coming from the Atlantic. It probably already overcame parts of New Jersey and areas like Long Island and Brooklyn, but they just showed it entering the harbor. As far as it coming from the east, the water probably hit the island of Manhattan and the east river probably also started to rise which would eventually overtake the island as well coming towards the library from the east.
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.
Suggested correction: According to Wikipedia, and other online sources, the Gutenberg Bible of the New York Public Library is publicly on display. It's shown in as being in a glass display case, there for anyone to see. There's no evidence that the book was taken for fuel. The first we see of it, it's being held by the person safeguarding it. It's possible they took it specifically to keep it safe. https://en.m.wikipedia.org/wiki/Gutenberg_Bible.
Suggested correction: He was the head librarian, and as such would have access to the safe/showcase. And he would want to keep the Gutenberg as close as possible to protect it.
That man clutching the Gutenberg was NOT a librarian, much less a "head librarian." He was just one of the civilians who came into the library to escape the climate onslaught. He wouldn't have access to something as precious and priceless as the Gutenberg. Original flaw remains valid.
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?
Suggested correction: She's the girl who was arguing with the man about which books could and couldn't be burned before the boy finds the section on law to burn.
Continuity mistake: When Sam and the others are walking in the rain toward the library, they are carrying backpacks or duffel bags, but when they reach the steps they are not carrying any extra baggage.
Suggested correction: The bags were slowing them down, so they probably just abandoned them in the street.
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.
Suggested correction: As already corrected, just because we can't see an outlet for the smoke doesn't mean there isn't one. White smoke against white snow is very hard to see.
Nik Rolls
But they were still burning the books, which meant the smoke should be black, if they stop burning the books, the smoke would have been white, which isn't the case in the movie.
Just looked at a boatload of videos of burning books, including one in a fireplace, and the smoke was indeed white.