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.
Character mistake: At the end of the episode, while Col. Potter is in the helicopter asking where they are, the pilot says they are about 10 miles west of Inchon. Col. Potter says this is no good and he tells the chopper pilot to "head west, towards Inchon." If they are already west of Inchon, heading west will take them further from Inchon.
Suggested correction: Potter tells the pilot to head to a different city, Chuksan (not sure of its spelling).
Continuity mistake: In this episode, a "Spirit Post" is placed in the middle of the compound, later removed, then replaced at the end of the episode. It is never seen again after that.
Suggested correction: It was probably left behind during one of the bug outs that happen. We have seen at least 2 in the series.