Hawkeye states he's an only child, after previously mentioning a sister in earlier seasons. In one particular mail call, she sent him an ill-fitting, hand-knitted sweater.
The exterior and interior of the Korean shack don't match up.
Hawkeye impersonates Laurence Olivier's performance as the title character in Richard III (1955). However, unless he saw Olivier in London or in Australia on the stage, he could not have known his performance as the film was released on April 16, 1955, 21 months after the end of the Korean War on July 27, 1953.