Audio problem: In the Post-Op ward, Jimmy is playing poker with the two jerks in his platoon. After the cards are dealt, he sees that their deck has pictures of nude women. He looks up at them when seeing this, and you hear him say "Very funny!", but his lips don't move.
Where There's a Will, There's a War - S10-E16
Revealing mistake: When Hawkeye injects the adrenalin into the chest of the dying soldier at the battalion Aid Station, you can see that he is actually injecting into a piece of rubber foam soaked with prop blood. (00:13:25)
Visible crew/equipment: In the scene following BJ's shower, when Hawkeye and BJ enter their tent, you can see the tip of the boom mic drop for a couple seconds.
Continuity mistake: When the Champ falls forward, he gets wine all over his sweater - you can see it when Potter and Hawkeye lift him. After the cut, his sweater is clean again. Considering the position of the stains relative to Hawk's hand, at least some stains would be visible. (00:08:10)
Answer: Even an Army field hospital would have SOME weapons for self-defense if the enemy attacked. What's meant is that it's not a combat outfit, and therefore wouldn't have enough weapons to actually attack anyone. (It's also mentioned a few times that the Officer of the Watch is supposed to carry a pistol at all times, but Hawkeye refuses to do it when he's in charge and Colonels Blake and Potter don't enforce the rule).
Captain Defenestrator