Factual error: When Klinger's walking with Captain Allen and the Stars and Stripes photographer, just before their introductions to "Ben" they pass an empty corrugated box with its flap open, and the recycling symbol can be seen on the flap. Recycling symbols were not in use until about 20 years later.
Other mistake: When Alan Alda and Mike Farrell are walking into frame in the scene where Hawkeye and BJ discover the huge shipment of tongue depressors, Alda's feet are visible for about two seconds and he has bright blue early '80s shoes on.
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