Factual error: In the scene where the guy is telling Machiko about the major league teams that wanted him, he mentions the Indians, Yankees, and Orioles. The episode is set in 1953 and the story is from before World War II. While there had been a minor league team called the Orioles up to that point, there was no major league team called the Orioles until 1954.
Revealing mistake: When Sam is first looking at his reflection of himself in the glass at the beginning of the episode, the items behind his reflection do not match his point of view. A man walks through the shot and never leaves the frame, however is gone when the shot flips back to Sam.