Continuity mistake: In the beginning of the episode Colonel Potter is painting a portrait of Hawkeye with his feet up, and Klinger's picture is hanging to the right of the door. But in the previous episode 'Korean surgeon' Klinger's portrait is on the left side of the door and the one of Hawkeye's is on the right side of the door, even though that portrait wasn't painted until the following episode. (00:03:15 - 00:17:55)
Continuity mistake: In the beginning, Colonel Potter is painting a portrait of Hawkeye. In the preceding episode, The Korean Surgeon, the painting is finished and hanging on the wall in Colonel Potter's office. It is hanging just to the left of the door. The time given is from The Korean Surgeon where you can see the painting hanging on the wall. (00:17:05)
Visible crew/equipment: As Potter and Hawkeye look at the totalled and burning jeep, the shadow of the camera's shade can be seen at the lower left corner of the shot.
Character mistake: As Potter and Hawkeye pull up to the MP checkpoint, Potter and the MP exchange salutes. As per Army regulations, no salutes are given under battle conditions. The reason is that if the superior officer, in this case Colonel Potter, returns the salute, he can be a target for snipers.
Character mistake: After Potter mocks Hawkeye for not hitting anything, Hawkeye replies "You fired as many shots as I did". In fact, Potter fired seven shots, Hawkeye only five. On a side note, this also suggests that Hawkeye probably was supposed to fire seven times, but his weapon jammed after the fifth shot. (00:22:00)
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