When Sid catches Tom running away at the beginning of the movie, he threatens to tell "Aunt Polly" and even tries to call out for "Aunt Polly" before being stopped by Tom. But for the rest of the movie, Sid simply calls her "Mother."
When Tom and Becky become engaged, they lean in one way to kiss each other, but in the next shot they're coming from the other angle.
When Tom is hiding in the old shed his shoe disappears and reappears between shots.
When Injun Joe places the treasure map on the table in the haunted house, it is folded up and slid under something else. In the next shot from Tom and Huck's view, it is unfolded and uncovered.
When Tom is cutting his finger, he cuts the index finger on his right hand, but in the next shot, he's writing his initials with the index finger on his left hand