There is Nothing Like a Nurse - S3-E10
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!" (00:18:10)
The Pin-Up - S7-E17
Stupidity: After Erin leaves with the military captain to Camp Lee, John and Maryellen turn around to see John Curtiss nowhere around on the porch where Maryellen left him. So John goes off to look for him, while Maryellen goes in to check The House. John Curtiss is a one-year-old baby who couldn't open a door.