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.
Character mistake: When Hawkeye asks Frank what he is doing, Frank replies he is lining up all bottles and jars "according to height and popularity". In fact, the bottles are not lined up according to height at all, also the order of condiments is different on the two tables. The sweet and sour gherkins Frank mentions are not there at all - during the pan shots you can see the line ends with the pepper. (00:01:50)
Character mistake: While talking to Condon, Hawkeye and Trapper relate the story of Dr. Charles Drew, the man responsible for the storage of blood and plasma, and how he died due to not being allowed in a "whites only" hospital after being involved in horrific car accident. The true story is that he was taken to a "poor whites" hospital. Despite being black, he was admitted, and though the doctors worked diligently, his injuries were too severe, and he died. His family sent a warm letter thanking the doctors for their efforts.
Character mistake: The last bet comes to Frank after Mulcahy bets a dollar, and Potter raises fifty cents, making it a dollar fifty. Frank makes it another five dollars, making it six dollars fifty cents. Mulcahy says "Oh dear, it's five fifty to me." He should have said six fifty.
Character mistake: As Potter and Hawkeye pull up to the MP checkpoint, Potter and the MP exchange salutes. As per Army regulations, no salutes are given under battle conditions. The reason is that if the superior officer, in this case Colonel Potter, returns the salute, he can be a target for snipers.
Character mistake: After Potter mocks Hawkeye for not hitting anything, Hawkeye replies "You fired as many shots as I did". In fact, Potter fired seven shots, Hawkeye only five. On a side note, this also suggests that Hawkeye probably was supposed to fire seven times, but his weapon jammed after the fifth shot. (00:22:00)
Character mistake: At the end of the episode, while Col. Potter is in the helicopter asking where they are, the pilot says they are about 10 miles west of Inchon. Col. Potter says this is no good and he tells the chopper pilot to "head west, towards Inchon." If they are already west of Inchon, heading west will take them further from Inchon.
Character mistake: Hawkeye and Trapper make Tuttle an alumnus of "Berlin Polytechnic" and translate that (wrongly) as "Berlinishes Polytechnikum". Berlin's polytechnic university was named "Technische Hochschule Berlin" at the relevant time - and at no time offered a medical curriculum. To study medicine in Berlin, Tuttle would have to attend "Freie Universität Berlin" instead.