When Charles pulls up to the house where the orphans live, frogs are croaking in the background. This is centered around Christmas. Frogs would be hibernating in December in Korea and therefore would not be croaking.
Trees with green summer leaves are visible in the outdoor scene where the truck from the orphanage arrives.
Although it takes place at Christmas in Korea, there is no visible breath when the characters exhale, although it must be very cold.
Loretta Swit's fingernails appear to be nearly 1 inch long. No nurse, especially a head nurse, would have fingernails that long.
The candy bar which Sgt. Rizzo procured from the black market is a modern, mass produced product similar to Toberlone rather than the small batch, handmade chocolate which Maj. Winchester described.
Klinger and the others wonder what is in the three packages Charles received, and he claims it was clothing. But when he drops the packages at the orphanage, Mr. Choi reads the name of the Confectioner off the address label. Thus the contents would have been obvious to anyone who saw the packages.
B.J., along with Hawkeye and Margaret, work tirelessly to try and keep the soldier alive so that his kids won't have to remember Christmas as the day their father died. However, being a MASH unit, they would be very limited on supplies, like blood and plasma, and they would not be wasted on a man who was already dead. If falsifying the date of death was the solution, Hawkeye could have just changed the clock right at the start, or they could verbally claim he died the day after Christmas.