The large columbarium (mausoleum for crematory urns) in the Gracey cemetery could not have existed because the first legal cremation in the United States did not take place until 1876, and the practice did not become common until the 1890s - long after the circa-1855 Gracey backstory.
A few jokes are made regarding Madame Leota's inability to move on her own. However, when Jim Evers is trapped outside the house (after being thrown from the attic) she seems to have the ability to roll along under her own steam. Of course, this is ignoring the fact that she'd need to be able to get out of the attic in the first place.
When the children are in the attic Emma is holding the tray of cookies. The cookies disappear when the children "must hide" and reappear in the hiding spot. There is an extended scene on the DVD that explains how the cookies appeared there.
When Jim's daughter is coming out of the water in the crypt after getting the key, a hand with a glove and a watch grabs her shoulder. It turns out to be Jim. However, in several shots before and after that, his hands are bare.
After the family get caught in the rain, they run up the steps to the front door and you can see the effects of the rain which include their wet clothes and Sara's frizzy, uncurled hair. Later, when they go into the house a few minutes later, her hair is again curled and their clothes are dry.
When Jim and the kids are outside the crypt you can see fog slowly creeping up towards them. Then when Jim and the daughter go inside and are trying to get out, the fog is at the sons feet. In the next shot or two the fog goes back to slowly creeping up upon them.
When Jim is thrown out of the mansion and lands on his car, all the the doors lock and all of the shutters on the windows close. However in the very next scene, the window shutters in the room are clearly open.
After Jim exits the painting and goes into the hallway, look down onto the rug. You'll notice dark lines on them, that's not part of the rug as they tried to make it look, it's the railings for the ride. They filmed it inside the ride, that includes the rails leading to the breathing door.
During the scene when Eddie Murphy's character finds the letter in the trunk a modern day spotlight is visible to audience left hanging down from the ceiling (When the camera is shooting upwards at him from the POV of the trunk.)