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: 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.