When the lawyer, Arthur Bell, meets North for the first time on the street, he hands North his card and promptly takes it back. In the next shot, North is still holding the card. At that point, Mr. Bell reaches to shake North's hand (which is still holding the card) and in the next shot the card disappears again.
Despite providing an extensive definition of Borscht, the movie fails to acknowledge the fact that it's a soup, so it's mostly liquid and unsuitable for distribution via cartons.
The divorce trial moves forward even though both of North's parents are catatonic. No Judge worth their salt would allow a trial of any sort to move forward when the defendants are clearly physically and vocally unable to defend themselves and would be deemed unfit for trial.
When North's Alaskan family is walking their grandfather to the shore, the ceiling of the studio the scene is filmed in is visible.
When North is being chased through a New York airport, he passes a neon eagle on the wall. This eagle is in the Los Angeles airport.
North behaves very out of character during the Amish scene, instantly bailing and not even giving them a chance because of their primitive lifestyle. All he was after was a family to love and appreciate him, and up until that point, the families he'd been with had unreasonable expectations of him, so whether or not the Amish family lived without electricity would be irrelevant.