Visible crew/equipment: In the scene where BJ, Hawkeye, and Radar are in the motorcade talking about the horse, Radar is talking about how he doesn't want to give away the horse. He is standing in front of some barrels and when he moves, you can see some of the crew, the horse owner, and what looks like another horse in the background for 1 second.
Factual error: In the scene where Hawkeye and BJ are actually fighting while pretending to fight; when they enter the tent, Frank is polishing his boots and whistling the theme music to The Muppet Show (1976). While The Muppet Show had already been screening for a year when this episode was first broadcast, the music was unknown in the 1950s as it was written specifically for the show by Muppets creator Jim Henson, and Sam Pottle.
Continuity mistake: After Iron Guts Kelly dies in Margaret's tent, Frank Burns visits Margaret, suspecting something. Frank asks why there is a general's star on her cot. In the ensuing 'back and forth' dialogue, Margaret's hair goes (in close ups) from nicely combed, to frazzled, back to nicely combed again (and in a different light).
Continuity mistake: When Hawkeye is examining the orphan who is wiggling his tongue, there are two camera angles: one of Hawkeye from the front and one of the orphan over Hawkeye's shoulder. In the first shot, the tongue depresser that Hawkeye is holding is horizontal, in the other it is vertical. This flips back and forth a couple of times.