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.
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 between shots. (01:04:20)
Factual error: When Sam climbs outside the ship he grabs the frozen metallic pipes and rails with both hands - one half covered with a glove, one is bare. He has no problem gripping the cold metal and he can get his hands free every time. If the moisture froze before contact, his hands would be frozen too, so that can't be the reason.
Factual error: The aircraft flying to rescue the British Royal Family are described as belonging to "an RAF search and rescue squadron." However the middle aircraft has white and green striped camouflage painted on it, which is a pattern only used by aircraft in 845 Naval Air Squadron (a Royal Navy unit).
Factual error: The football (soccer in the U.S.) match we see relatively early on in the film is said to be between Manchester United and Celtic, in Glasgow. However, the non-MU team isn't wearing Celtic's home strip as they should be if playing in Glasgow (it's actually Boca Juniors from Argentina, in a match played in 2002) and the stadium shown is actually Old Trafford, Man. U's home ground, as shown by the advertising billboards in the background. (00:09:25)
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)
Continuity mistake: The first time we see the black bear cage, the sign (and the entire shot) is a reversed image. Twenty five minutes later, we see the black bear cage again and the sign is correct. (00:20:35)
Revealing mistake: Very near the end of the movie, when the NOAA director is viewed in the helicopter as it approaches NYC, the image is reversed, verified by the David Clark logo on his headset being reversed. There are two different shots of this just a few seconds apart, and they are both reversed.
Continuity mistake: When Sam and his two teammates are on their way to NYC for the competition, the airplane gets hit by turbulence. Two attendants go to the back of the aisle with the drink cart, when the plane starts to shake, and in the long shot of the aisle (from the head to the back) one of them is in front of the cart and the other one is behind. However, both are behind the cart in the close up, when they try to prevent the cart from hitting anybody.
Plot hole: When you see the shot of New York, just before the scene where the apartment lights go out, there are no lights on in the buildings, or car lights in the street, although it is dark. The lights should still be on as there has not been a power outage. (01:28:00)
Continuity mistake: When Jack is trekking north to Manhattan with two of his colleagues, one falls through a glass ceiling and the other cuts his right hand trying to save him. Despite the fact that we see his hand bleeding profusely, you can see in the subsequent scene that his right hand is just fine.
Factual error: NOAA headquarters is shown to be in downtown D.C, when in fact it is just outside of the District in Silver Spring, Maryland.