Factual error: When the can of beans explodes all over Hawkeye and Hotlips, they act as though the beans are cold. In fact the beans would have been at boiling temperature as the can overheated, causing it to explode, and the two would have been burned.
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.
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