Although there are plenty of clearly intentional anachronisms throughout the movie (jackhammers, references to Mark Twain, Blazing Saddles, etc.), King Richard's coat of arms (quartered English lions with blue fleurs de lis, introduced after 1485) is likely to be unintentional.
When Robin sings "The Night is Young and You're So Beautiful" he exclaims "Bb" before he starts to sing (in reference to what key the music should be played in). The song however is in the key of E major and modulates to F major, not Bb.
During the "Men in Tights" song and dance number at the lyrics: '...We roam around the forest looking for fights...', Dave Chappelle (Ahchoo) makes a minor mistake in choreography by raising his right-hand to his forehead instead of his left-hand, and then makes a quick switch to correct his mistake.
When the Sheriff goes into the throne room to tell Prince John about Robin attacking him, John tells the woman in the blue dress "Later...!". She giggles and runs away. In the next shot, she runs away again.
When Robin cuts the side of Sheriff of Rottingham's saddle, it all slides underneath the horse with Rottingham, but when the camera looks back up at Robin, the saddles seat is clearly visible on top of the horse but when the camera cuts moves back to the whole scene, the saddle seat is again underneath the horse with Rottingham.
At the end of the movie, as the camera zooms out, the location of the Loxley castle seems to be in the area of London. Sherwood Forest (where the story is set) and Nottingham are in the East Midlands area which should be a bit further North.