At the airport when boarding the plane at 46 minutes in, the baby switches to a completely different baby. In the next shot they are on the plane and the baby has switched back.
After Mel has crashed the truck and is at the police station, Paul and his partner leave the questioning room. When they re-enter the questioning room, Paul opens the door with his left hand. In the next shot, he is entering with a clipboard in his left hand.
The amount of brie cheese that Mrs. Coplin is waving at her husband.
The shoulder with the towel and the baby.
The shots of airliners flying overhead (to symbolize the characters flying across the country) are Boeing 727s. By 1996 when this movie was made, 727's had long been taken out of passenger service.
Cameraman visible in mirror in detectives office.
When Mel and Nancy are in bed at end of movie and get a call that Mel's parents are in jail there is a microphone boom shadow on the lamp and wall (by the shape of the shadow the microphone appears to be a "Schoeps").
Tony calls Paul "Phil" when they are in the restaurant, just as Paul gets up to leave.
At the end of the movie, when they are at the jail, the baby goes from asleep to awake in different shots.