Binghamton says he will send McHale and his crew to Leavenworth. The Army's prison is in Leavenworth, Kansas. The Navy's prison was at Portsmouth, New Hampshire.
The story is built around Parker's new tape recorder, something which did not exist during World War Two, outside of (German) experimental ones.
In imagining what a possible radio show he and Parker might produce together, Binghamton offers that it might close with his saying, "Good night, Chuck," and he respond "Good night, Wally." This is a reference to the then-famous "Good night, Chet", "Good night David" coda to The Huntley-Brinkley report, NBC's evening TV news broadcast from 1956-1970.
In addition to tape recorders not existing outside of some German ones,
portable ones the size Parker has here didn't exist until the early 60s.
The German experimental ones in WW2 were suitcase sized monsters.