When Martha May gives the engagement ring back to The Mayor, she holds the ring box out to him while he looks at the ring and her with his arms by his side. In the next shot, Martha May has her arms by her side while The Mayor is holding the ring box in both hands.
When the Grinch finished loading his sled, he had turned all the Christmas lights off. As he was trying to take off, all the lights were on, but his sled stalled. His second attempt of taking off all the lights were off again.
The goof item below may give away important plot points.
The narrator says the Grinch's heart is two times too small, then later the Grinch checks and says it's down a size and a half, making it three and a half times too small. So then, even though his heart grows three sizes, it would still be half a size too small, and the Grinch would still be mean.