Factual error: After the opening credits it cuts to Klinger at Mail Call, and Father Mulcahy's reading Ring Magazine which is dated December 1969, 16 years after the Korean War ended.
Visible crew/equipment: While in the mess tent, after Margaret's grossed out by the smell and walks away we hear Charles start playing again, and when Colonel Potter says, "Just make sure the three of you work this out fast," in this shot we can see the actor's T-mark on the floor between Potter and Hawkeye, where Margaret stood a moment ago.
L.I.P. (Local Indigenous Personnel) - S2-E7
Continuity mistake: When Lieutenant Willis wakes up in the Swamp and puts his shirt on he's wearing his dog tags, but when he tosses the papers and puts on the rest of his clothes the dog tags have suddenly vanished, then they reappear, vanish, and reappear again.
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: When Radar walks into Henry's office to tell him that there's a general there to see him, we get a good view of Henry's new desk and its beautiful ornate design, but later when Hawkeye and Trapper are carrying the desk and then it's lifted out by chopper it's a completely different desk - also note that this desk has casters.
Goodbye, Farewell, and Amen - S11-E16
Continuity mistake: Early in the episode a tank is driven into the MASH compound by a wounded soldier (demolishing the latrine in the process). The tank is an M24 Chaffee dating from the mid 1940s - it is squat and angular in shape. Later on in the episode after the tank has been hidden under a tent Hawkeye decides to drive the tank into the camp dump (demolishing the new latrine on the way). The tank has changed into an M4 Sherman - it is a lot higher and more rounded in shape.
Requiem for a Lightweight - S1-E3
Continuity mistake: The bag used by Trapper for training is marked "Property of MAJ. Frank W. Burns". However, later in the series Frank's middle name is revealed to be Marion.
Continuity mistake: Radar hangs the hammer on the "Out of Order" sign and it is covering the 'of'. When he and Frank walk away the hammer has moved and is covering the 't' (00:15:20)
Continuity mistake: When Radar is slipping the glass of milk into Buzz's tent, we see the outside of the tent and there are no windows. From the inside, the milk is placed on a table that is right under a window. Also, the milk is already on the table in a scene before Radar puts it there. (00:13:20)
Continuity mistake: In some shots, Radar's exam questions are in his hand, in others they are tucked under his arm. (00:10:30)
Continuity mistake: When Radar and Burns leave the tent for morning parade, Radar's clipboard acquires a pencil. (00:02:50)
Continuity mistake: The length of the chewing gum hanging from Henry's hat differs between the front and rear shots. (00:03:10)
Continuity mistake: After Iron Guts Kelly dies in Margaret's tent, Frank Burns visits Margaret, suspecting something. Frank asks why there is a general's star on her cot. In the ensuing 'back and forth' dialogue, Margaret's hair goes (in close ups) from nicely combed, to frazzled, back to nicely combed again (and in a different light).
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.
Visible crew/equipment: When Frank and Hot Lips are walking into the mess tent for Frank's surpise party, if you look in the window to the right of the door, you can see a person silhouetted, throwing leaves into the wind.
Continuity mistake: When Frank is trying to examine the Colonel, in some shots Buzz's robe is open and in others it is tied at the waist. (00:10:50)
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.
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