Throughout the movie, a mole on the face of Prince John (Richard Lewis) changes position: it starts on his left cheek, then over to his right cheek, then his chin, then his forehead. It then goes back to the original place. This lampoons the mole on Alan Rickman's face in Robin Hood: Prince of Thieves (1991). It's also a nod to the famous "I-gor's hump" gag from Young Frankenstein (1974).
The gag about Robin being able to speak with an English accent is a reference to Kevin Costner's performance in Robin Hood: Prince of Thieves (1991). Unfortunately viewers who saw both movies in a dubbed version couldn't get this gag. For the German dubbed version the gag was changed to: "because I - unlike some other Robin Hood - do not cost the producers 5 million". The German word "kosten" (cost) was also pronounced to sound a little bit like Costner. In the French (France) and Italian (Italy) dubbed versions, it is translated as, "Because unlike other Robin Hoods, I do not dance with the wolves", referring to another Kevin Costner movie Dances with Wolves (1990). In Quebec, the translation becomes "Because unlike other Robin Hoods, I accept to wear tights," which refers to the fact that Costner didn't wear tights in the 1991 movie.
There is a rumor that the idea for this film came when a studio executive turned to his son and jokingly demanded "Give me an idea for a sure-fire hit, or else!" The boy replied "That's easy. Do a parody of Robin Hood."
When Ahchoo first appears, he and Robin fight Prince John's knights with a style Robin calls "Praying Mantis". Praying Mantis is an actual martial art - a style of Kung Fu emphasizing grabbing your opponent and bringing him to the ground - but it is nothing like the slapstick techniques that Robin and Ahchoo use.
The character played by Joe Dimmick, "Dirty Ezio", was originally written as "Dirty Harry" (Dimmick being a Clint Eastwood look-alike). But on that shooting day, Ezio Greggio, the Italian director, was visiting on the set and Mel Brooks decided to change the killer's name as a joke-homage to his colleague.
When Robin Hood first comes across Ahchoo, he is being beaten by a group of soldiers, and Ahchoo says, "I hope someone is getting a video of this thing." This is a reference to the Rodney King beating in the early 1990s, when a group of L.A.P.D. officers beat a black motorist and a bystander captured it on video. The acquittal of the officers sparked the L.A. riots.
When attempting to motivate the villagers, the speech given by Robin Hood is a clear reference to two speeches given by Winston Churchill during WWII, specifically the "We shall fight them on the beaches" (given after the British withdrew from Dunkirk) and "Never was so much owed by so many to so few" (given after the Battle of Britain).
When the the crowd gives Robin the chop at the archery tournament, this references a tradition at the Florida State University sports matches. The chant is also sung when at FSU games. The chop was also, prior to this film, brought to more focus with the Atlanta Braves baseball fans adopting it to cheer on their team in the League Champion and World Series.
In the Jerusalem prison, when the head guard Muktar asks Chuchim for the tongue looseners to use to get Robin Hood to talk, three of the other prisoners gasp in horror, and at the same time, mimic the "See-no-evil Hear-no-evil Speak-no-evil" pose.
When the newly recruited Merry Men are getting outfitted with clothing and weapons, their tights are seen being taken out of giant plastic eggs. This is in reference to when L'eggs pantyhose used to be sold in plastic eggs packages.
When Prince John is in his bathtub and the Sheriff asks him if the mole wasn't on the other side, Prince John replies "I have a mole?" According to some images, Prince (later King) John Lackland really had a mole on his right cheek.
The trivia items below may give away important plot points.
Patrick Stewart plays King Richard talking in a thick Scottish accent, a reference to Sean Connery's performance in Robin Hood: Prince of Thieves (1991). Some critics found Connery's accent inappropriate for the role, since King Richard would not have spoken with a Scottish burr (thus providing comedic fodder for Mel Brooks). Technically, an English accent would have been no more appropriate than Sean Connery's Scottish accent and a French accent would have been best for Richard (and any other nobles of the time, possibly including Robin), as "English" did not yet exist as a language and English nobles spoke Anglo-Norman, a dialect of Old French, while the common folk spoke Old-English, an Anglo-Frisian tongue that has more in common with Old Norse than with Modern English.