This episode was the second episode to be completely digitally colored (instead of colored traditionally through cel animation) but third episode overall, a practice that would later be used starting with the season 14 episodes,"Treehouse of Horror XIII" and "The Great Louse Detective." The first was season seven's "Radioactive Man." However, Season 7's "The Simpsons 138th Episode Spectacular" also used digitally colored for the original animated content in the episode, and can count it as the second digitally colored episode.
The episode title is a pun on the comic strip (and movie) Dennis the Menace (The American version, not the British version).
When the tennis tournament puts Homer and Bart into competition over who gets to have Marge as a partner, Lisa makes a reference to Oedipus.
When Andre Agassi introduces himself at the tennis match, Homer asks, "The wrestler?", confusing Agassi for professional wrestler André the Giant.
Grandpa sings the "What's New Pussycat?" theme by Tom Jones at the talent show, replacing "whoa whoa whoa" with "Ow, ow, ow, ow" and "Oh, God, no!" having injured himself while attempting to dance.
In the supermarket Lou refers to Homer and Marge as the Los Angeles Clippers of doubles tennis. At the time (early 2000s), the Clippers were regarded as the worst NBA franchise in history.
Homer mistook tennis for foxy boxing, but didn't know what it was called. He referred to it as "the sport where the chicks whale on each other." Previously, however, in "Lisa on Ice", Homer knew the name of the sport (when he was telling Lisa that girls should stick to "girl sports," like hot-oil wrestling and foxy boxing) and earlier in, "Homer's Night Out," Homer took Bart to a strip club that was hosting a foxy boxing match in his search to find Princess Kashmir and apologize to her.
However, given Homer's mental capacity (and the terrible continuity of the show), he (and the writers) could have easily forgotten.