Barney's hair alternates from messed up to straight between shots, as he is reciting the Preamble to the Constitution.
The closeups of Barney as he's reciting the preamble to the Constitution show his hair as frazzled and unkempt. In the next shot, his hair is neat and combed.
In the episode "Bringing Up Opie", it's made clear that apple pie is Opie's favorite pie. In this espisode, it's stated that his favorite pie is butterscotch 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.