Audio problem: When the bulb in the projector goes out, Klinger is trying to fix it. People throw popcorn at him, saying "Find it!" After Potter says "Hit it, Father!", watch Klinger. From the wide shot to the close up, you hear him say "The bulb is hot!", but his lips don't move.
Other mistake: After Klinger douses himself with real gas (Potter determined that Klinger's can only had water in it, and told Radar to switch the can for real gas), and runs into the shower tent, you hear a nurse scream, and see her run out. When the door is open, there are no stalls to be seen. From all scenes shot inside the tent, you know that the stalls are big enough to be easily seen from the outside.
Continuity mistake: After a distant aerial shot of Potter's chopper, the camera closes in for a close up. When in the distance, the rotors are running full speed. In the close up, they are barely running, just enough to make the familiar whooshing sound. The chopper that they are in is being raised and lowered to simulate flight. Also, if you look in the canopy in front of Potter, you can see the camera and crew's reflection. Then when the chopper is over the building, the sound of the blades is still the slow moving whooshing mentioned earlier, instead of the full power sound it should be.
Revealing mistake: When Hawkeye and Margaret turn toward the stove, and he says "Are you hungry?", watch the can. Though it is meant to look like it blew the top off, it is plain that the top was just set into the top, and a blast of air was used to blow it open. This is because of the sound, and a stream of vapor that often accompanies a blast from an air gun. A sealed can set on a heat source would have burst not only from the top, but also from the side at a seam, or the bottom. Also, they were about five feet away from the can, and the beans went up, not out at a ninety degree angle. So they wouldn't get beaned. Beans on the face were for comic effect.
Continuity mistake: When BJ, Hawkeye and Radar are being shot at, they hurry to get in the jeep. Radar gets out to get the jack, and salutes it. When the camera cuts to a shot of Radar getting back in, the jack is magically gone. It doesn't appear again.
Revealing mistake: Toward the end of the episode, Henry is talking to a general on the phone when the chopper is coming in. He's trying to tell the man that he can't hear him. As he continues trying to talk, he gives up, and hangs the receiver up on the skeleton's head. If you look, you can see the hook that was conveniently placed for the gag.
Plot hole: Hawkeye calls a number of people into the mess tent over the PA - the ones he allegedly suspects of being behind the thefts he is suspected of himself. Interestingly enough, Ho Jon, later revealed to be the guilty party, is not on Hawkeye's list - yet he shows up uninvited, just to be ensnared by Hawk's clever ploy. Note also that he had no way of knowing what the purpose of the meeting was, so we cannot ascribe to him the motive of wanting to find out how much Hawkeye knew.
Plot hole: When the truck with the orphans arrives, Col. Potter and Nurse Cratty greet each other like one would an old friend. Being new to Korea, Col. Potter doesn't know Nurse Cratty - as becomes clear from his reaction to Hawkeye's explanation to BJ earlier (who doesn't know Nurse Cratty for the same reason, but that's not relevant for this mistake). Note that in other parts of the series Col. Potter is depicted mostly as somewhat old-fashioned and reserved towards strangers.
Factual error: The MP describes the antique vase Burns is supposed to have bought as "An 800-year-old seladon vase of the Ko-Yu dynasty". Later, Burns packs up a white vase to send to his wife. Seladon is by definition green, and that kind of color glazing definitely wasn't around in the 13th century. What Burns packs up looks most like early to middle Quing period - or rather a contemporary ripoff.
Plot hole: When Hawkeye and BJ buy Margaret a new ring, it takes a typo in the inscription to give them away - which makes both of them and Mr. Shin almost clairvoyant. Not only did they somehow guess Margaret's ring size, but Mr Shin - phew, Houdini and Uri Geller together don't hold a candle to this guy - actually somehow divined the exact type and font of the inscription in the original so perfectly that Margaret actually only spotted the difference from the missing 'n.'