The scenes aboard the aircraft carrier were filmed aboard the U.S.S. Yorktown (CV-10). As evidenced by the number 10 on the superstructure.
Max, as an officer, is addressing sailors, and when he turns the camera focuses on his hand, in which he is fidgeting with steel balls, a tribute to "Captain Queeg", the captain played by Humphrey Bogart in The Caine Mutiny.
James Komack, Director of this episode, played photographer "Uncle Norman" on MGM's "The Courtship of Eddie's Father" starring Bill Bixby and Brandon Cruz.
The Chief's navy uniform has the name "John Doe" on it.