Continuity mistake: When Hawkeye's saying goodbye to the nurse in the morning, he reads "35591715" from her dog tag and says, "Even your number is pretty," and then he makes another date with her and again reads her dog tag, but now the number's "39591715."
Visible crew/equipment: While Margaret's reading the story of 'The Three Bears' to Kim, just as Frank walks into the tent the curved chalk foot mark can be seen on the floor.
Other mistake: When Hawkeye and Trapper are arguing with Henry about not sending the little boy to the orphanage, Henry says, "Look, you think I wanna send this little fella away? I got two kids of my own. I'm a former child myself," but at the end of season 1 Henry's wife delivered a boy, whom Henry was aching to be with, so Henry really has three kids.
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