The Funnie's neighbors are the Dinks. Their name stems from the acronym D.I.N.K. which stands for "double income, no kids". This is a slang term that refers to a childless couple where both people work and are, therefore, more affluent than families with dependents.
In the episode where Doug and Skeeter form a garage band, they wear oversized suits to a gig at a birthday party, a homage to the Big Suit worn by David Byrne of the Talking Heads in Stop Making Sense (1984).
Doug's favorite band, "The Beets", is an obvious reference to The Beatles, most notably the lead singer (who bears a striking resemblance to John Lennon) and the drummer (who bears a similar resemblance to Ringo Starr)
Sometimes, Doug would write up comic books of himself when he "daydreams". One of them is Quail Man, though not a reference to any pre-existing comic book hero, but Quail Man wears his underwear over his pants, poking fun at most heroes in comic books that have an "underwear" shape design on their costumes.
Judy Funnie's name may come from the poem "Shakespeare's Sister" written by Virginia Woolf. In the poem, Woolf states that if Shakespeare would have had a sister, her name would have been Judith. Furthermore, Shakespeare himself had a daughter named Judith. Since Judy Funnie is obsessed with Shakespearean plays, it is possible that this is why her name is Judy.
A poster above Doug's bed shown prominently in many episodes features a sinking ship with the phrase "LOOSE LIPS..." emblazoned above the ship. This is actually a famous World War II-era propaganda poster, depicting a sinking ship with the words "LOOSE LIPS SINK SHIPS" discouraging civilians from carelessly talking about friends or relatives fighting abroad, as supporters of the enemy could overhear conversations and relay any useful information from the conversation, such as troop position and formation, to the enemy's advantage.