Continuity mistake: Adam picks up his head from the table and puts it back on. In the following shots the blood around the neck and head has disappeared.
Continuity mistake: At the start, when Adam drives to the store a fireman is cleaning the right side of the fire truck. A shot later he's now cleaning the front part. Also, when he exits the store the two firemen swap places between shots.
Continuity mistake: As Barbara recoils after getting hit with the steel plate over her mouth, she starts to move back just before, and repeats the move just after, it appears.
Continuity mistake: When Beetlejuice is screaming at Barbara and Adam, he kicks over the model tree. As he does, his hands are close to his sides. In the closer shot, they're a bit further out from his sides in preparation of the crotch grabbing joke.
Plot hole: Jane badly wants to sell the Maitland home, so it's not practical that she left all of their furniture, decorations, and other possessions after they died. Any realtor who wanted to make a quick sale would have the place cleaned out, instead of leaving so much stuff for the new owners to deal with.
Suggested correction: Actually, it's not all that uncommon for realtors to sell fully furnished and "staged" homes. And depending on the location and market, they sometimes sell quicker than unfurnished homes, since it means that it's less for the new buyers to purchase. This especially makes sense, since Jane seems to like the idea of selling the house to a larger family who might desire such things. As for their possessions? There was probably no family who wanted them, and Jane probably just hadn't gotten around to getting rid of them yet, since the Deetz family seems to move in rather quickly after the Maitlands died. I feel like at best this is a "stupidity" or "character mistake", but I'd argue it's neither.
Suggested correction: Jane tells Lydia that she "personally decorated that house," so it's not impossible that she was maybe looking to be hired as the new decorator.
I always thought Jane was lying when she said that she decorated the house. The Maitlands were quite offended when the Deetzes began to change everything, as if they decorated the place themselves, and chose/inherited the furniture. I think Jane was nosey and wanted to keep getting attention for herself. But this is just how I interpret it.
Continuity mistake: When the wedding clothes are laid out for the seance, there are no pants/trousers in place for Adam, but when he materialises he has them on.
Continuity mistake: When Charles is looking out of the window, he pushes one slat of the blinds upwards, and then bird watches with his binoculars. When Lydia comes in and makes him jumps, he turns around, and this particular slat falls back downwards, into place. But in the very next shot this same slat is pushed in an upwards position again. When he sits back down again as Lydia leaves, the slat is back down again. (00:27:35)
Other mistake: When Adam and Barbara have their sheets on, trying to scare the mother, they walk out in failure and Lydia takes pictures of the ghosts - polaroid photos fall out (too quickly) and Lydia picks up one which is already developed - they take longer. (00:39:25)