In the opening scene, Barney is trying to get Andy to remember what important event happened to Barney 5 years ago that day, May 16th. Later that day, as Aunt Bee, Thelma Lou, Floyd and Opie are making preparations in the courthouse for Barney's 5th Anniversary surprise party, the one-page calendar next to the gun cabinet clearly displays the 15th. Thirty seconds later, they all hide in the back room just a few seconds before Barney walks into the courthouse. A moment later, when they all rush out with the cake and holler "Surprise!," the calendar now reads "May 16." No one had the opportunity to tear off the "May 15" page.
Near the end of the episode, Barney comes into the sheriff's office wearing his civilian suit to go to the weigh-in. But when he and Andy come out of the inspectors office, Barney is wearing his deputy uniform, without the tie and hat.
While Barney is hanging from a harness to stretch his spine, Thelma Lou enters to offer him a milkshake. In a rare (likely accidental) bit of product placement, the shake is in a Baskin-Robbins cup, with their "31 Flavors" logo emblazoned on its side. Fictional Mayberry had no chain stores, including what was, in 1964, still a regional ice cream franchise founded in Glendale, CA.
Barney confirms to Andy that the standard uniform is required to be worn, without shoes, for his physical. However, he doesn't wear the tie, as Andy does, which would be part of the standard uniform.
When Barney shows up for his weigh-in, there is a fellow officer named Hansen, who is just finishing his physical and gets approved by the inspector. That officer is clearly shorter than Barney, who was already in jeopardy for being too short to begin with.
Everybody is celebrating Barney for serving five years with the Sheriff's Department. However, in the episode "Citizen's Arrest" from season 4, Andy and Barney talk about how he'd had been a deputy for ten years.
In all previous episodes in which Frank Thompson's character, Asa, appears, his last name is given as "Breeney." However, in this episode, his last name is given as "Bascomb" and he is without his signature mustache.