When Maggie Taylor forgets the kitten's name, it was not a part of the script. Mae Whitman actually forgot the kitten's name and stayed in character. The director thought that it was so cute that he kept it in the movie.
The school that was used for the scene where Jack and Melanie find their children's class had already left is a private college called the New York School of Interior Design or NYSID. The red front doors were added for the filming.
The press conference scene where Jack confronts the NYC Mayor is supposed to be in City Hall in Manhattan but was actually filmed in Brooklyn Borough Hall which is the office of the Brooklyn Borough President.