Stupidity: Hawkeye and Trapper park a jeep over a foxhole to trap Maj. Burns in it. While it is certainly possible to trap somebody in a hole with, say, a sports car, an off-road vehicle like a jeep is particularly unsuited for the task - the chassis has so much ground clearance, even a quite fat man could squeeze out past it. You can even see the gap when the camera cuts to Major Burns screaming "Let me out!"
Stupidity: When an officer is speaking to who he thinks is colonel Tuttle but is really Radar with a surgical mask, he says what he needs to and is about to leave. Radar who was alone at the time and was completely in on the fact that Tuttle never existed, could have kept up the façade and let him leave, but instead chooses to reveal himself which was utterly pointless.
Stupidity: Radar takes his glasses off, takes a sip of coffee, then props his clipboard onto the typewriter and accidentally starts typing on the desk calculator. Even if he didn't know his desk well enough to wonder what he laid his clipboard upon AND was so blind he couldn't even orient himself by the desk lamp (which he isn't), he would have felt the difference the instant he touched the keys. Note that he puts his hands on the keys, squints at the clipboard (sic!), then starts typing, he doesn't hammer away right off, which would have added at least a little plausibility to the joke.