Character mistake: When Henry is describing the fishing reel he bought for his girlfriend, he said, "with jeweled escarpment" actually it is a 'jeweled esCAPEment" not esCARPment. An escarpment is a long slope off a plateau. An escapement is a latch/release mechanism that you would find on a device like a fishing reel.
Other mistake: When Henry gives Leslie the gift he says, "I sent to Tokyo for this... A Sato Tanaka double-cammed reel with jeweled escarpment," and we can see on different sides of the box there's green tape hiding its brand name, "Penn," though we can still make out the "Beachmaster 155" name.
Other mistake: When Frank's with Margaret in her tent and she tells him that she thinks they should reevaluate their friendship, there's a Life Magazine lying on her bed which is dated over 15 years in the future - August 25, 1967, with "The other war in Vietnam" written on its cover.
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.
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.
Factual error: The announcer says that it will be the 53rd Army-Navy game, but the game has been played every year since 1890, with no games in the years 1894-98, 1909, 1917-18, and 1928-29, so this game would be number 51. Additionally, at the end of the episode we find out the result was Navy 42 - Army 36. While Navy won all three games during the Korean conflict, none of those games ended with such a score. The score in the 1950 game was 14-2.
Continuity mistake: As Henry is receiving his medal, Hawkeye walks up and stands close behind a man who is standing up and two women who are sitting down. The camera angle switches to show Hawkeye talking to Trapper and now they are standing behind two standing women. (00:03:55)
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: 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.