The distance between the bars on Tweety's cage keeps changing every time Sylvester grabs the cage. The cage also changes from having both horizontal and vertical bars to just having vertical bars and back again several times. Finally, the door in the cage disappears and reappears several times.
When Sylvester cuts the hole around Tweety's cage and the ceiling falls down there is ceiling trim still up around the room.
The next scene shows no ceiling trim anywhere.
When Thomas/Sylvester starts coming down the chimney, there are logs in the fireplace. However, when Tweetie goes to put logs in the fireplace, there are none.
When Thomas raises himself up to the cage with the fishing rod, Tweety's pose changes completely between the wide and close shots.
Near the end of the short, Thomas throws a broom in the fireplace. Rather than it burning up, it simply vanishes between one frame and the next.