This episode was digitally colored, the third attempt after season 7's "Radioactive Man" and "The Simpsons 138th Episode Spectacular". However, the crew held off on completely switching over to digital coloring so that they could further fine-tune the process.
When Homer asks if Andre Agassi is "the wrestler", it is a reference to the late wrestler André René Roussimoff known by his ring name Andre the Giant.
The title is based on the newspaper single panel comic "Dennis the Menace" that has been produced since 1950 and started by the late Hank Ketcham.
The second episode of season 12 with the word 'menace' in the title, after The Computer Wore Menace Shoes (2000).