Visible crew/equipment: After Howard heads to the TV show with the bird, when it cuts to Aunt Bee and Mike in the car the reflection of the boom pole and mic can be seen on the car's rear windshield, and we see it moving again when they all drive away.
Aunt Bee's Cruise: Part 1 - S1-E15
Revealing mistake: Aunt Bee is traveling on a cruise ship. The "water" in the background is a painted backdrop which is made all the more obvious by the painted whitecaps.