The tank initially driven into the camp by the wounded soldier is an M-24 Chaffee light tank. When Hawkeye later drives the tank out of the camp, it is a Sherman tank.
When everyone is saying what they will do after the war, Luther Rizzo says he plans to raise frogs to sell frog legs to French restaurants. It was established in several episodes that Rizzo was a career Army man. He actually reenlisted in Season 9 and therefore would not be leaving the service at the end of the war with everyone else.
The injured tank driver was clearly not the same man being operated on in the next scene.
When Hawkeye is returning to the 4077th, he and the driver read "Burma Shave" signs that were set up to welcome him back. After they pass the signs, an ambulance comes speeding up behind them, honking its horn. After driving forward a little bit further, Hawkeye's driver swerves to the left to give them room, and the ambulance swerves to the right, somehow managing to knock over all of the Burma Shave signs that had already been completely passed a few seconds earlier.
Near the end, the Jeep driver who takes off with Margaret reappears in the background when B.J. and Hawkeye are about to salute Colonel Potter.
When Hawkeye gets out of the tank, he gets out from the commander's cupola, not the hull, meaning he could not have been driving.
During the farewell dinner in the mess tent, Nurse Kellye is wearing her rank and medical insignia on the wrong lapels on her uniform.
When Margaret and BJ are hugging as BJ is leaving, Loretta Swit's fingernails are over an inch long. No nurse, especially a head nurse, would have fingernails that long.
Hawkeye's illness and hospitalization are triggered by an event on a bus. The bus was crowded and full of people. It seems impossible that no else saw the event (and the reason for Hawkeye's illness). It is however likely that everyone is already aware of the cause of Hawkeye's illness (except him). When Hawkeye finally remembers and recounts the event on the bus, Dr. Freedman reacts in a manner that suggests he already knows.
BJ rides off on his motorcycle. This brings up questions of how far he can get and how he is going to get home. The 4077th MASH near Uijeongbu is about 15 miles from Seoul, so it's fair to assume that BJ will make it that far without needing to stop anywhere for gas, and that he will be able to figure out his travels from there.
During the bug out, Radar can be seen helping to remove a trunk from a building. This is due to the reuse of footage from the episode "Bug Out," but does not fit in the continuity of the show as Radar was sent home to Iowa during season 8.
Colonel Potter's horse, Sophie, is supposed to be a mare. In the shot of Potter riding "her" away from camp, "she" is definitely a male horse.
In the series installment "Hey, Doc", a Sherman tank is called in to simply park at the 4077th to scare off a sniper. In this movie, Potter wants the tank that ends up in camp gone because it would draw fire.
When Margaret says she's got a nursing job at NATO's headquarters, everyone says she's off to Belgium, but NATO's headquarters was in Paris when the Korean War ended and only moved to Brussels in 1966 when France quit the military structure of NATO.
The pilot of the chopper that carries Hawkeye is wearing Nomex flight gloves. These were not used until 1967 during the Vietnam War. In Korea, pilots would have worn black leather gloves.