The entire premise of this installment is ridiculous. The M*A*S*H stoves are fueled by wood, not natural gas.
The camp's equipment would not have broadcast to Frank's radio.
The announcer states that Gil Hodges hit a 3-run homer in the 9th inning to beat Sal Maglie and the New York Giants. During the entire span of the Korean War, June 1950 to July 1953, Gil Hodges hit 3-run homers against the Giants. Two of them were hit off Sal Maglie (oddly enough, in the same game: August 16, 1950), but they occurred in the 3rd and 8th innings, and the Dodgers still lost the game, 16-7.
Maj. Overman tells Hawkeye that he'll be back "on Friday" to check on his progress -- which means that Hawkeye will be bandaged and out of action as a surgeon for at least several days. Yet the 4077th is not sent a replacement surgeon, and there is even an O.R. scene showing only the three remaining surgeons at work. Regiment would never let a hospital be short a surgeon for several days; it would be catastrophic if the 4077th were inundated with casualties.
Hawkeye and company broadcast the baseball game over the unit's radio while Frank listens in his tent. He is listening on a transistor AM radio, of which the technology wasn't available during the Korean War. Also, the camp's radio system would likely broadcast in FM mode, which if heard within the confines of the camp would be very clear without the static heard on Frank's end.
In his tent, Frank listens to the ballgame on a portable transistor radio, as shown by its size and that it starts playing as soon as Frank turns it on. Transistor radios were not sold until 1954, after the active fighting in the Korean War.
Maj. Overman, the ophthalmologist, wears glasses with 1970s frames not available during the 1950s.
After Hawkeye is injured, Col. Potter gives Radar instructions about calling for an ophthalmologist and to get him here pronto. While Potter is speaking, Radar is also speaking, saying the same things at the same time, the way he usually does, but his voice is not heard.