Visible crew/equipment: When Klinger walks into Henry's office while Margaret and Frank are there, we can see the chalk T-mark on the floor behind Margaret where Radar was standing moments ago.
Continuity mistake: Right after Radar tells Henry to forget about the game there's an explosion, and when Radar shouts, "More on the way!" everyone ducks and we see Henry's diploma up on the wall, but when it cuts to a different angle the diploma has vanished before the room even shakes or the heater's stovepipe falls.
Continuity mistake: While Radar's spying on Baker's hand for Hawkeye during the poker game, Baker's only wearing his T-shirt later in the game, but in the views from Radar's telescope eyepiece Baker's still wearing his jacket.
Continuity mistake: In some shots the Spam lamb has mashed potato eyes and a carrot mouth, in others it has green grape eyes and no obvious mouth, and it keeps changing. (00:23:10)
Continuity mistake: When Radar is going to bed, he takes his shirt off and his upper body is naked. When he puts the blanket over his teddy bear you can see sleeves. Next shot, he is naked again.
Revealing mistake: When the mail arrives in the compound, in daylight, everyone has 3 shadows. (00:00:50)
Continuity mistake: Margaret is shampooing Frank's hair; she raises her foam covered hands to allow him to kiss her. The camera angle changes and her hands are nearly foam-free. (00:03:25)
Revealing mistake: When Baker is talking with Father Mulcahy it is clear that Baker's nose is prosthetic. The colour doesn't match as well as it does in other scenes. (00:05:45)
For the Good of the Outfit - S2-E4
Revealing mistake: Frank is shaving; when he bends down to pick up the envelope containing shrapnel fragments, the foam on his face and ear suddenly all dries up. The shot must have needed a lot of takes. (00:07:20)
Continuity mistake: When Margaret pins on Frank's purple heart, his scrubs are very damp with sweat. When he enters the swamp, they're practically dry. (00:03:50)
Continuity mistake: When Frank is getting drunk he spills gin down the front of his vest. A few shots later, just before he collapses, it suddenly dries out significantly. (00:13:20)
Sometimes You Hear the Bullet - S1-E17
Continuity mistake: Frank and Margaret are dancing in her tent when Frank's back seizes up; in the subsequent shots sometimes his arms are around her waist and sometimes around her shoulders. (00:02:30)
The Trial of Henry Blake - S2-E8
Continuity mistake: In the scene of Klinger trying to escape from the 4077 on a hang glider, he secures himself into the control frame, but then when he takes off, he's hanging off the frame's bottom bar. (00:10:40)
Continuity mistake: At lunch, when Frank is getting his own back against Hawkeye, in the long shots of the table the plate of bread is beside Henry and in the closeups it is in front of Trapper. (00:11:30)
Visible crew/equipment: After Radar shows the box of bees to BJ and Hawkeye, when BJ gets in the jeep and drives off, just before the shot cuts away we can see the T-mark on the ground at Radar's feet.
Continuity mistake: During the shelling on the road, BJ gets very muddy. When they get to the bar, he is much cleaner - e.g. all the mud has disappeared from his right arm. (00:44:30)
Henry, Please Come Home - S1-E9
Other mistake: While Radar's in post-op waiting for Henry's arrival he's seen reading Marvel Comics "Captain Savage and His Battlefield Raiders!" issue #10, published January 1969. It's one of the 19 issues in this comic book series which were originally named "Captain Savage and His Leatherneck Raiders," and it ran from 1968 until 1970, many years after the Korean War ended. This comic is also seen in the episode "Tuttle" later this season.
Visible crew/equipment: When Trapper and Hawkeye walk into the Swamp and find Dr. Pak waiting for them, the edge of the tent set can be seen at the top left corner of the screen.
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