Moulin Rouge/WMG

Zidler is Satine's father.
Red. Hair.
 * Don't forger all the sweet nicknames that he calls her with.
 * Not to mention "I dont need you anymore! ALL MY LIFE youve made me believe I was only worth what someone would pay for me!" And his reaction to finding out she was dying before remembering as creatures of the underworld, they cannot love...

Chocolat loves Satine as well.
He's always there to step out of the shadows and save her when she needs it. Almost as if he were, say, stalking her...
 * Or alternately, he's basically there to spot her in case she injures herself during a performance, but over time found himself falling for her. Also, Satine's costume-changer kid with the raccoon eye makeup totally has a thing for her too.

Christian is dying of tuberculosis.
Think about it. It's well-established that Satine has tuberculosis when we first see her, and the disease can be spread through infected saliva. Keeping in mind how much... contact she and Christian had, there's a good chance that he got the disease as well. Christian realizes this, and writes their story so that his memories of her will live on after he has died too.

Aside from the Can-Can scene and Hindi Sad diamonds scene, all of the trippy musical numbers are in the heads of Christian and his friends.
They halucinated a green fairy when they had a shot of absinthe each. This also explains the frantic editing at the start of the film, they were all on absinth but stopped once the situation with the Duke became serious. Elephant Love Melody? Christian trying to make the scene where he and Satine fall in love more romantic.''
 * This is almost but not quite confirmed by Word of God: all the musical numbers were meant to be viewed as events and songs of the time as viewed through a modern lens, changing them into songs the audience would be familiar with so as to invoke the proper emotional response people of the time would have had (example, using "Smells Like Teen Spirit" for the society men to sing to represent how wild and crazy and decadent the Moulin Rouge was--the actual songs of the time wouldn't have sounded like that to us). It's only a slight jump from this to suggest these "modern songs used to convey an old-time feeling" were also just in the characters' heads.

The events we see are also distorted by Christian's writing
Compare Henri de Tolouse-Lautrec singing 'Nature Boy' to him during the rest of it. He's very different. It's possible then that Christian has also exaggerated all the characters in the story to make it more exciting, while keeping the narrative the same.

Nini and the Argentinian had a relationship in the past.
During the "Tango de Roxanne", the Argentinian seems genuinely angry about a failed relationship with a courtesan. He sings this song to Nini and tangoes with her, becoming more violent as the tango progresses. When Nini tells the Duke that she doesn't understand why Satine's character in Spectacular Spectacular would fall for a penniless citar player over a the Maharaja, she is implying that she wanted to be with the Argentinian, but the money in dancing and prostitution was better.

The entire film was in Toulouse's mind while he was locked away in the sanitarium
Explains why he knew everything, how the handkerchief plan worked so perfectly, and perhaps lampshaded in his opening song singing alone about all that is happening.
 * Satine is the redheaded cortisone he painted so many times.
 * Check out that Other Wiki for some brain popping >>> http://en.wikipedia.org/wiki/Henri_de_Toulouse-Lautrec

Nini Legs-in-the-air's real name is Roxanne.
During "El Tango de Roxanne", she seems shocked and a little hurt when the Argentinian calls out "Roxanne". Why? Because it's her real name, which she had only told him. This is his way of slut-shaming her.