Other mistake: When Frank's with Margaret in her tent and she tells him that she thinks they should reevaluate their friendship, there's a Life Magazine lying on her bed which is dated over 15 years in the future - August 25, 1967, with "The other war in Vietnam" written on its cover.
Other mistake: After Klinger gives the long johns to Mulcahy, he "disappears." But if you look closely through the camo net, you can see him in the shadows of the background.
Continuity mistake: When Henry is put on the table, he rolls onto his back while requesting gas. After a cut to Hawkeye, he's on his stomach.
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