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.
Character mistake: After the robots first attack New York City, a series of newspapers is shown. One of the headlines in the French one reads "La Tour Eiffeil est détruite". The proper spelling is "Eiffel" (00:15:55)
Character mistake: In the start of the film, the sticker on Peter's head for his work misspells the word Bleecker Street on it.
Character mistake: When we first see Sophie her body was slumped over (the spell to make her old) but later on in the movie, her back magically seems fine. (00:00:01 - 01:50:00)
Character mistake: Jill states that a 5 kiloton nuclear weapon will sanitise the city, however, such a yield is far too small to destroy the city. (00:42:00)