Visible crew/equipment: There is a unknown 3rd person helping Charles and Otho remove the model from the attic. You can see him briefly just as the scene ends on the left side of the screen moving the front portion of the model, closest to the camera, between us and Charles. Charles and Otho would be hard put to move that entire model by themselves. Otho says it is sectional, but they still seem to move the entire model in one piece.
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.
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)
Answer: They died by drowning. Jane's daughter even tells Lydia when she asks what happened. Although Adam and Barbara should have been completely wet for the whole movie, Tim Burton decided to keep Alec and Geena dry as he felt that keeping them wet the entire time would be an uncomfortable experience for both of them.