After several unsuccessful attempts by director Les Landau to film Q's nude scene without forcing the actor to actually be naked, a frustrated John de Lancie finally asked anyone offended by nudity to leave, stripped down, and filmed the scene in one take.
John de Lancie's favorite appearance as Q. He reportedly said he had legitimate fun on set. It was also his last appearance before the release of Taking Care of Business (1990) where he appeared with Next Generation co-star Gates McFadden (Dr. Beverly Crusher}.
This episode contains the "Picard face palm" scene which became an internet meme.
John de Lancie actually filmed his nude scene standing upright in front of a blue screen. His horizontal position was a special effect created in post-production, with Captain Picard positioned strategically in front of him.
The mariachi band was playing the folk-song "La Paloma" (Spanish for "The Dove"). The English version is called "No More" and was made popular by Elvis Presley in Blue Hawaii (1961).