At the beginning, right after Christian sings the 'hills are alive' line, the unconscious Argentinian says something about him having lots of talent, and 'happens' to put his hand on his crotch. Then later in the movie, when Satine is unbuttoning his pants when they are in the elephant for the first time, she calls him a 'big boy' and Toulouse says he has HUGE talent.
Baz Luhrmanns films have the on going theme of "L'amour" or forbidden love. Not only in Moulin Rouge, but also in Romeo Juliet and Strictly Ballroom, the red "L'amour" sign can be scene in the background as part of the set. The L'amour sign was a set piece from Baz Luhrmanns first staging of La Boheme and he puts it in every one of his movies.
In the scene when the Duke asks for the ending of the play to be changed, look in the background and you'll see an elaborately decorated horse. this horse was originally supposed to be in the production (as proposed in the 'Spectacular, Sectacular' number). The floor was specially reinforced for the weight of the horse but for some reason the horse's scene was cut from the movie and he can only be seen in two short shots.
Originally, the green fairy was going to be a long-haired muscle man with a giant sitar, and Ozzy Osbourne was hired to provide the vocals. Eventually it was changed to the current "Tinker Bell" incarnation, played by Kylie Minogue, but Osbourne still gives voice to the fairy's guttural scream when it turns evil.