Deliberate mistake: These errors I assume were caused by the show running 3 times longer than the real war. Col. Potter arrived at MASH in September 1952 a year before the war ended, then a few months passed by Margaret got engaged for 8 months, then Frank Burns left and Charles took his place. In this time the war would have ended. In the final episode Margaret mentions Charles has been there for 2 years. Which means he would have arrived in 1951 a year before Trapper and Henry left and Col. Potter arrived. It's a lot to take in.
How to Win Friends and Influence Nazis - S3-E7
Deliberate mistake: Burkhalter pulls some papers out of his bags marked "Top Secret." Why would German papers be marked in English, so the prisoners know what not to look at?
Deliberate mistake: Around the 26 minute mark, when Charles Brandon joins Margaret for a game of cards during their voyage to Portugal, Margaret has a glass of wine (and later Brandon) in which the liquid is not sloshing around As It Should Be on a ship that is rocking and swaying the way it should. (00:26:10)
Containment - S1-E11
Deliberate mistake: Sunny is the teams SAW (squad automatic weapon) gunner. He carries an FN MK46 which is a special operations version of the M249 SAW. The MK46 unlike the M249 only takes belt-fed ammunition from 100 or 200 round "nutsacks." On this mission Sunny is wearing a chest rig with STANAG mags and no nutsacks. He has no backpack for extra ammo either. He hands off his MK46 to the Jason whose staying behind and no nutsacks. Plus he doesn't take Jay's HK416 rifle in the swap. Usually people swap one for one. (00:31:15 - 00:32:00)
Mercy Moment Murder Measure - S1-E7
Deliberate mistake: When Abraham throws the secret note into the fire, he crumples it up before tossing it in. But then we see a shot of the note lying open and flat on the log before burning. Not only would the note not be able to uncrumple itself, it shows no sign of being crumpled in the first place. This was obviously done deliberately so the audience could read the note one last time.