At the beginning of this episode, Aunt Bee allows Opie to skip drinking his milk at breakfast. Barney later expresses his disapproval of this to Andy, which is puzzling because Barney wasn't even at the Taylors' house when it happened.
After Andy helps Barney recite the preamble to the Constitution, Barney gets himself all worked up and messes up his hair. Opie then walks in, and Barney is suddenly sitting calmly with his hair perfectly combed.
When Opie is observing his new bicycle you will notice that the bell is on the right side of the handle bars, but watch closely and you will observe it switch to the left side mysteriously and then magically it returns to its original position.