The Abduction of Margaret Houlihan - S5-E6
Other mistake: As Frank cocks his gun in the Swamp, the slide locks open and he has to hit the slide release to get it to move forward. Next he fiddles with the hammer. Next we hear the shot go off. Burns' excuse later is that he was cleaning The Gun and it went off (although admittedly, Frank doesn't always stick to the truth that religiously in situations like that). The slide on a semi-automatic locks open only if the magazine is empty or missing. The Gun locking open is also a clear, unmistakable indication that the breech is empty. He would have to insert a filled mag, then pull the slide back again to chamber a round before The Gun even had the chance to go off. One never does that while cleaning a gun. One does what Frank did to begin with: Pull the slide back without a magazine inserted to make sure the breech is empty.
Suggested correction: Frank has demonstrated on numerous occasions that he does not follow the rules of safe gun handling, so ascribing his failure to do so is not a mistake.
You are missing the point. His gun is demonstrably unloaded when we last see it. He would either have to change his mind about cleaning it and load it instead, or load it first and then try to clean it (which makes even less sense), neither of which is not supported by anything in the dialogue.
Dear Sigmund - S5-E7
Other mistake: As the ambulance takes off rounding a corner, the back brightens as stage reflectors or lighting rigs shine on it.
The Most Unforgettable Characters - S5-E14
Other mistake: After Klinger douses himself with real gas (Potter determined that Klinger's can only had water in it, and told Radar to switch the can for real gas), and runs into the shower tent, you hear a nurse scream, and see her run out. When the door is open, there are no stalls to be seen. From all scenes shot inside the tent, you know that the stalls are big enough to be easily seen from the outside.
Other mistake: When Hawkeye finds the New York Times Crossword he says, "1 down, four letters..." and "1 across...four letters..." and BJ's answers are "chap" and "cast" but in the shot of the newspaper puzzle we see that both "1 down" and "1 across" are actually five letters each, not four.
Other mistake: When the four nurses at the door sing, two are singing, two accompanying. The nurse on the right of the shot seems to have forgotten the words.