Audio problem: In the Post-Op ward, Jimmy is playing poker with the two jerks in his platoon. After the cards are dealt, he sees that their deck has pictures of nude women. He looks up at them when seeing this, and you hear him say "Very funny!", but his lips don't move.
Continuity mistake: When the boys are working on the vascular clamp, Charles brings out three hard boiled eggs. After he heckles BJ and Hawkeye for a minute, BJ takes the hammer, and smashes Charles' eggs. The camera cuts to the boys, and back to Charles. There are now two eggs, and almost intact.
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.