In the episode "Henry in Love" from earlier in the second season, Henry Blake is on the phone with his wife discussing her financial situation. She wants to send him her cancelled checks so he could balance her checkbook. At the end of the phone call, he agrees to her request. In "Mail Call", Henry receives a box of cancelled checks and other financial documents from his wife. This is apparently the result of the phone call from the earlier episode.
In this episode we learn Trapper's daughter's names are Kathy and Becky.
Hawkeye gets a sweater from his sister. This is the fourth time said sister is mentioned between Season One and Season Two. Yet, in future, he's referred to as not having any siblings.
During mail call, Radar's clothes are stripped off in the commotion. This is similar to Charlie Brown's clothes coming off when his pitch comes back too quickly to field. Gary Burghoff played Charlie Brown on Broadway.