When Jerry is on top of the 8 ball, Toms lights the triangle Jerry's jumping through on fire. Oddly, the part where Tom's hand is doesn't catch on fire.
In the opening shot, Tom puts three balls on the table and tries to shoot one of them into the corner pocket. The camera pans with him as he tilts the table in order to succeed. The camera pans back, and the other two balls are exactly where they were before.
When Tom is groping around in the pool-table pocket trying to find Jerry, there are a couple of split-second moments when his tail disappears.
The ball rack, previously burned by Tom in the beginning of the cartoon, is perfectly fine when Jerry uses it to rack up the balls near the end of the cartoon.
When Tom shoots the striped blue ball, it has no number on it. When Tom shoots the same ball down the pocket and it hits Jerry on his head, it suddenly has the number "10" on it. Update: Based on the size of the stripe on the red (11) ball, the blue ball that Tom shoots is really the completely blue (2) ball (completely, that is, except for the number spots), which becomes the blue-striped (10) ball when it falls down on Jerry.
When Jerry is pushed out of the hole and into the table rack, the two balls in the upper rack are the 4 and 6 balls. The 4 ball should be purple, not blue.