Continuity mistake: After the Grinch stole all of the presents, Officer Wholihan gets into his police car and drags the mayor's bed from out of his house. When the bed smashes through the window it breaks the top off the middle post of the bed. Then when it comes back to the shot of the bed it's been fixed.
Continuity mistake: When the Grinch is messing up the mail in the back room, he takes out a package and puts it in another one. When he takes his hand out the package falls out and lands next to the pile of presents. The mistake is when the camera goes to another shot, the package is not lying on the ground as it was before.
Visible crew/equipment: The movie was filmed in a large set to recreate Whoville, but in the mayor's first appearance, if you look in Lou Who's glasses, you can see a stage light from the ceiling above.