Gomez is wearing a checkered jacket when he lets Morticia operate the controls to his trains but when they show the trains heading towards each other from a different angle you can see Gomez's arm and he is wearing his regular pin striped suit.
The broken-off cup handle Ophelia pulls out of the sink is round at first, then changes to an angular shape when Gomez takes it from her.
When Gomez first pulls off his winter scarf there is nothing on his inner shirt scarf. But in the next shots we see a big silver scarf pin holding it in place.
When Thing hands Gomez Morticia's present, he is a left hand instead of his usual right, as when he hands her the scissors just moments later. When he flips the train switch, he is also left.
When Grandmama explains about being high school friends with Hester Frump, she is facing Gomez. It then cuts to a longer shot, and she is facing Morticia.
(at around 7 mins) When Gomez opens the conservatory door for Morticia, he places his hand inside the cutout for the glass. This reveals the fact that the prop door does not actually have glass in it.
When Thing throws the switch to stop the train he is completing the circuit and it should have been the other way.
At 10:25 exterior view is reversed.
Gomez and Morticia swiftly improvise the idea of crashing the trains and blowing them up at the same time. It is presented as if such a stunt had not previously occurred to either character. So why was the explosion plunger already set up?
Morticia is shown feeding her Cleopatra plant in 1952. Yet in The Addams Family Meet the VIPs (1964), Gomez said that Cleo is "3 years old, and she can't even feed herself yet," suggesting that Cleo was born/planted/germinated in 1961. (Maybe Morticia has had a succession of Cleopatra plants.)