Robert De Niro wanted "Mr. Jinx" to appear in more scenes than he was supposed to because De Niro liked the cat so much. Apparently, De Niro would also play with the cat between filming scenes.
The MPAA would not allow the name "Focker" unless the filmmakers could find an actual person with that surname.
Robert De Niro originally wanted to train the cat himself, but then realized that would take up several months of his life. Instead, he would carry kibble in all of his pockets, which helped him enjoy a very cooperative relationship with the animal.
At one time, Jim Carrey was slated to star as the lead and even contributed jokes to the screenplay, such as the main character being named "Focker".
(at around 1h 19 mins) According to the DVD commentary, the car chase scene was originally meant to be a spoof of Sát Thủ Tự Do (1998). When the filmmakers got to the location, they saw how quickly the lights changed, realized it would be a funnier joke, and re-wrote the scene (the lights really did change from green to red as fast as they are shown in the movie).