Patty is actually a lesbian, as revealed fourteen seasons later in "There's Something About Marrying", which would explain her "celibacy" and reluctance to date Principal Skinner. Also, in the Season 2 DVD Episode Guide, the episode description mentions that "Patty rejects Skinner (and possibly all men)."
In this episode, Skinner implies that Bart is the only boy in Springfield Elementary with that name.
Skinner points out the Board of Education, which is a paddle, meaning the school once allowed corporal punishment - then again, most schools used to. And the name of the paddle is a common joke referencing said punishment.
This is the first episode the short version is used with "D'oh!"
Skinner yelling, "Tomorrow is another school day!" parodies the last line from Gone with the Wind: "Tomorrow is another day."
Homer profiling every man to find Selma a date is similar to the film The Terminator.
The title is a parody of Prince Charming, a fairy tale character.
The movie Principal Skinner and Patty see on their date, "Space Mutants V: The Land Down Under", in which a marsupial variant of the space monster (with a baby alien in a pouch) attacks Australia, is a reference to the werewolf movie Howling III: The Marsupials.
When the line is shown for the DMV Barney is shown, right after Homer talked to him, unless Barney happens to live close to the DMV.
Otto Mann is in the line for the DMV. But in The Otto Show in Season 3 we learn that Otto never had a driver's licence, so what's he doing there? DMVs also distribute non-driver's license identification cards; he may have been getting one of those.
In this episode, Lisa states she is eight, however, she didn't turn eight until the season 3 episode, "Stark Raving Dad". This is because the series is a floating timeline, where the characters do not age physically.
Skinner claims he and Patty are going to the premiere of a Space Mutants movie. This series is apparently huge and popular in the Simpsons universe. Movie premieres are typically crowded events with a lot of fanfare, but this appears to just be a typical slow weeknight show without too many people there.