It's unlikely that a M*A*S*H unit would have had "The Moon Is Blue" but not impossible. "The Moon Is Blue" was released July 8, 1953 and the Korean War didn't stop until July 27, 1953.
The Moon Is Blue, the film watched in this episode, did not come out until late 1953, a few months after the Korean War had ended.
Klinger: There's no end to this furnace. Baste me once before I die.
Hawkeye: Didn't you inherit the heat-resistant blood of your forefathers?
Klinger: They cut my family out of the will when we moved to Ohio.
B.J.: Why don't we forget the movie and just have a sweating contest?
Klinger: (In full uniform) Hi, guys! Nice day, isn't it?
B.J.: Will you look at him? He's shelveled.
Hawkeye: Klinger, have you been seeing an air conditioner behind our backs?
Klinger: No need to, Doc. Thanks to those pills you gave me, I'm cool as a cucumber. I'm going for some coffee; can I get you a cup?
Hawkeye: You crazy? (Klinger exits) Looks like I've discovered the cure for the common hot.
(the camp is watching The Moon is Blue)
Hawkeye: I'm outraged! It's a disgrace. I've never seen a cleaner movie in my life.
BJ: There was more filth and dirt in this morning's breakfast.
Father Mulcahy: Well, one of the actors did say "virgin."
Hawkeye: That's because everyone was.
Hawkeye: I thought you went to see Sahara tonight.
Charles: Indeed, I did. But, alas, I had to leave when the film broke which was about two seconds after I ripped it from the projector. And I would have been here sooner but I had to stop to accept the cheers of the entire audience.
Hawkeye: The only good thing about being here is that we're able to drink and forget that we're here.
Hunnicutt: It's a good job we're doctors, 'cause your movies are making us sick!
General Rothaker asks Col. Potter why is there a speakeasy in the camp (referring to the Officers Club) and would tell Col. Potter to shut it down. General Maynard Mitchell had it constructed as an appreciation of Hawkeye and Trapper John operating on his son in the episode "Officers Only" (9/22/73). Not sure how this General could close the Officers Club when another one opened it other than Rothaker asked if the Officers Club was staffed by Special Services personnel, which it wasn't. Maybe that's the "out" the writers used to explain how General Rothaker could close General Mitchell's club. The Officers Club's original bartender- Kwang Duk- might have been Special Services although it wasn't established at the time but he didn't have any other role at the 4077th. The actor who played Kwang Duk (Clyde Kusatsu) returned in that same role for "Henry in Love" (1/5/74) and later played Sgt. Michael Yee in "Goodbye Cruel World" (2/11/80) and Capt. Paul Yamato in "The Joker is Wild" (11/15/82).
The camp gets the movie State Fair in this episode, which co-stars a young Harry Morgan (Colonel Potter).