We never find out what business Lt. Baker had at the 4077th.
A number of cast and crew during the first season were veterans of Hogan's Heroes, which ended its run a year earlier. Writer Laurence Marks wrote over 60 episodes of Hogan's Heroes. Both John Orchard (Ugly John) and William Christopher (Father Mulcahy) had guest roles on Hogan's Heroes. In later seasons of M*A*S*H Bernard Fox made an appearance, as did Sandy Kenyon and James Gregory--all having appeared on Hogan's Heroes earlier. Gene Reynolds directed 34 episodes of Hogan's Heroes.
The method Hawkeye and Radar used to cheat at poker, watching the other's cards with a telescope while relaying the information via an earpiece, is the same as in Goldfinger (1964). In that movie the game was gin.
After winning The Moose in a poker game, Hawkeye mutters "dear dad" ... as if he was writing a letter to his father to describe the camp's happenings. This "letter home" concept would be repeated throughout the series.
This show, along with several others, includes Ho Jon, which makes no sense because in the pilot Hawkeye raised $2000 because he was accepted to medical school and was going to stay with Hawkeyes family. There was never a show featuring his departure. They simply wrote him out with no explanation.