Continuity mistake: When he's talking to Cindy Lou in the Post Office, Lou is riding on the movable ladder, When he says "You kids and the Grinch", he's right at the end of the track when the camera cuts to Cindy Lou. When it cuts back, he's just stopping at the end. The sound while the camera is on Cindy Lou suggested that the track was longer than it was.
Other mistake: When Martha May is getting ready to put up her lights with the cannon, she pulls a charging handle, and starts firing. If you watch closely, you see a lit string of lights come out, but the spool that they're on isn't moving, or lit up. Then after all of the lights are out, it still fires several more times (watch the aiming indicator- it continues to flash with the sound).