When Richie approaches Fonzie by the Nip It pinball machine, the machine score board/back changes from an ornate image with people to a very plain image with an alligator.
At Arnold's, Arnold walks away from Richie, Potsy & Ralph who are at a booth. Ralph has a football in his hand as he sits down. The next shot shows Richie now holding the football (he had none previously).
After Fonzie reads the Japanese message at Arnold's wedding, there's a shot of Arnold's bride's chaperone smiling, and he's standing alone. In the very next shot, he's surrounded by people.
The "Nip-It" pinball machine (which inexplicably changes backboards) was produced in 1973, not the 1950s.