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.
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: Football matches shown on TV are never cut well into the 2nd half to be "welcomed back" at 63 mins. And no British commentator would say "Glasgow, Scotland"? In the UK we know Glasgow is in Scotland. He would say the stadium name - Celtic Park.
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.