After Sherlock Jr. spins the fence around, placing his pursuers behind it, he puts a crossbar across the gate to stop them from coming back. In the next shot, as he leaves the alley, the crossbar is no longer visible on the fence.
While playing pool, the placement of the balls changes between his shots, the cutaways, and his next shot. Sometimes balls even return to the table.
During the pool game, The Butler switches out one of the pool balls. Even in black & white, it's obvious the two "13" balls have a different colored stripe. Also, the "9" ball, which is a yellow-striped ball, has a much darker stripe than it should. This probably was done to enhance the contrast.