Revealing mistake: When Hawkeye and Margaret turn toward the stove, and he says "Are you hungry?", watch the can. Though it is meant to look like it blew the top off, it is plain that the top was just set into the top, and a blast of air was used to blow it open. This is because of the sound, and a stream of vapor that often accompanies a blast from an air gun. A sealed can set on a heat source would have burst not only from the top, but also from the side at a seam, or the bottom. Also, they were about five feet away from the can, and the beans went up, not out at a ninety degree angle. So they wouldn't get beaned. Beans on the face were for comic effect.
Continuity mistake: When BJ, Hawkeye and Radar are being shot at, they hurry to get in the jeep. Radar gets out to get the jack, and salutes it. When the camera cuts to a shot of Radar getting back in, the jack is magically gone. It doesn't appear again.
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)
Continuity mistake: While Igor is serving dinner, his cap peak goes from being up in the front shot to down in the side shot, while he is talking to Col. Potter.
Continuity mistake: At several points, in the second half of the episode, you can see the identification number (2A401) on the general's jeep that Hawkeye stole. As well as the big star, showing it to be a general's jeep. At the end of the episode, Col. Potter shows up for the first time, in the same jeep.
Goodbye, Farewell, and Amen - S11-E16
Deliberate mistake: BJ mentions to Charles that if they don't sign the armistice it will be the second time in 2 years and then he will miss his daughter Erin's second birthday. This is BJs 7th season and when he arrived at the beginning of season 4, Erin was already born, making it absurd that seven years later she could still be one year old. Because the real war lasted 3 years and the show 11, there are obviously some errors like this that can't be avoided but this was blatantly egregious.
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