Barney's hair alternates from messed up to straight between shots, as he is reciting the Preamble to the Constitution.
In the episode "Bringing Up Opie," it's made clear that apple pie is Opie's favorite pie. In this episode, it's stated that his favorite pie is butternut pecan.
Aunt Bea says she baked Opie's favorite pie, Butternut PEE-Can. No one who is native to the South refers to the nut as PEE-Can. The correct pronunciation would be pee-CAHN.