When Thing hands Max a comb, he is a left hand instead of his usual right.
Uncle Fester identifies the leg sticking out of the swordfish on the wall as Cousin Squint, even though in The Addams Family Tree (1964), Gomez explained it was Cousin Farouk. However, Fester could be mistaken as several other family members of the Squint family tree are mentioned throughout the series. It is also possible Farouk was one of the Squints.
When Pierre the Moose's antler's are moving, the string controlling the left one is visible.
Obvious jump in the film when Max's toupee fixes itself on his head.
When Gomez and Morticia are consoling Uncle Fester after Madelyn Smith walks out on him (at around 22 mins), there is obvious overdubbing when Morticia's voice says "just your kind," but her mouth pronounces "the right kind."