June says to Beaver, "Do you know that Uncle Billy will be flying all the way from California?" This is another instance indicating California as a distant state, but it was clearly shown that Ward has California license plates on his car in Beaver's Doll Buggy (1961).
On the door to Mrs. Rayburn's office, it states "PRINCIPALS OFFICE", with no possessive apostrophe. It should state "PRINCIPAL'S OFFICE". It's a mistake one shouldn't see in any school, especially on the door to the Principal's office.
Mrs. Rayburn says that four diplomas are missing from her desk. When she finds them in her drawer, she reads off five names instead of four.