Revealing mistake: When the tent roof caves in and the projector shorts out in a gush of water from above, you can see that actually the projector "shorts out" before the tent roof ruptures. The crew probably didn't want to risk the pyrotechnic devices getting wet.
Factual error: Henry says that every Wednesday, his wife drives up Route 26 with some friends. US. Route 26 starts out in Nebraska and leads to Oregon. The closest thing that could be described as a "Route 26" would be the road leading from Princeton, IL to Dixon, IL which begins 85 miles from Bloomington. The writer probably meant Route 24, which passes about 20 miles north of Bloomington.
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).
Other mistake: Hawkeye, Henry and Trapper are playing scrabble. The board is in an illegal state - in the lower right corner 'it', 'jot', 'joy' 'yearn' and 'in' are not connected to the rest of the words. Since the others call Hawkeye on his non-existant word, I'm assuming they're playing properly.
Continuity mistake: In one of the earlier episodes Henry becomes the father of a baby boy; his other two children have been established as Molly and Janey, both girls. In "Abyssinia Henry," Henry get his discharge papers and wanted to call home with the good news. He tells Radar that he will have to wait a while, as his son, Andrew, will be practising his trombone. As Henry only has one son, Andrew has to be the son who was born while Henry was in Korea. Even if Henry was in Korea from the very first days of the war, by the time he left his son can't be any older than 18 months - hardly likely to be playing a trombone.