In the scene where Homer is trying to sign up for the Naval Reserve, he questions an officer about a question that was scratched out. This was a reference to the Don't Ask, Don't Tell policy that Bill Clinton proposed where he would allow gays in the Armed Forces, as long as they were not openly gay in the military. Consequently, the Armed Forces were no longer allowed to "ask" soldiers if they were gay (hence the question now being crossed out and the officer trying to avoid hearing Homer answer the question).
Bart sings a portion of the song "Do the Bartman" and Ralph Wiggum comments that it "is so 1991", a reference to the year the song became a hit in the U.S.
It was difficult for the writers to figure out how to get the captain off of the sub and they eventually decided to have him shot out of the torpedo tube, which in the DVD commentary, Al Jean says that Rod Steiger claimed that he really did get stuck in a torpedo tube once.
This episode was written in 1995 and produced in 1996, as it was part of Al Jean and Mike Reiss's second stint as show runners in the mid 90s. it still bears a 1998 copyright year in the credits, which matches the 1998 air date. Other episodes from this production line however have copyright years which don't correlate with air dates.