Continuity mistake: When Jack is briefing the President, he draws a line on a map of the U.S. and tells the President to have everybody south of that line evacuated. The shape of the line changes three times between shots. (01:04:20)
Trivia: There is a party at J.D.'s school after the academic decathlon. Most of the students are wearing name tags. Sam's name tag says "Hello my name is Yoda." (00:21:50)
Factual error: When the North Atlantic current is shown on a world map, there are a couple of errors on it. 1) South East Asia is missing, and 2) Arabia is joined to Africa.
Visible crew/equipment: When the janitor is approaching the door you can see a shadow of a man, which isn't the janitor's, in the background holding something that appears to be a microphone. (00:30:05)
Continuity mistake: When Jack and Lucy are talking about Sam failing class on the phone and Lucy says "I don't have time to talk about this right now", it shows Sam eating and a milk pack with its opening pointing left. When it cuts the opening is pointing right. (00:12:25)
Continuity mistake: When the huge tidal wave hits the bus you see a man standing on top of a taxi, number 7Z22, which gets crushed by the water. Moments afterwards you hear the French woman saying that she left her bag behind. If you look on the right side of Laura you can see a still intact taxi with the number 7Z22 on it. (00:47:30 - 00:48:00)
Continuity mistake: When on the plane and there's the major turbulence Sam's hair flops over his forehead.Then he looks at the wing and there is no hair on his forehead but in the next shot of him his hair is back messed up. (00:17:55)
Continuity mistake: At the end of the movie, when they are all in the helicopter, it cuts to a view of them looking out the window. In this shot, the black actor is sitting next to the window, on the other side of the helicopter, but in the following one, he has suddenly switched seats, and is no longer sitting next to the window. (01:49:40)
Continuity mistake: When we get to the public library the first time there is a shot from behind the homeless guy - he has his hand on a cart. When it cuts to a front shot his hand is off the cart. (00:44:25)
Continuity mistake: When the man asks Jack "Why for the love of God would you aggravate the Vice President?", he has both his hands up. When it cuts his hands are down. (00:13:20)
Continuity mistake: In the scene where Sam smashes the vending machine in the library, you see him first take out about three items from it, and then in the next shot you see him holding two items, but when he throws them onto the table there are about a dozen packets of sweets and crisps. (01:11:25)
Continuity mistake: When the tidal wave is about to hit Manhattan, Sam and his two friends are walking up the stairs, and the black friend's hood is over his head, but in the following shot it is no longer over his head. (00:46:35)
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)
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.