This movie knows the power of the cross-cut. Unfortunately it doesn't seem to be aware of the cross-cut's weaknesses.
Moulin Rouge is at its best is when it is cross-cutting within the scene. The opening and closing twenty minutes are superb. Cross-cutting within the scene highlights suspense - since many actions are happening at once - and texture - because it shows the layers of a place and a moment.
But cross-cutting within the scene is by its nature horizontal. To go horizontal you have to have a strong narrative drive to support the sideward movement. This script has no story drive between the opening and closing sections. So it collapses under its own weight.
The story stalls at the song "Like a Virgin". Why? Because the creators are hitting the same beat; the hero has already won his goal, the girl, so all that is left is fooling the dim-witted opponent again and again.
This film shows what happens when you ignore the basics of storytelling and go for the flash. Moulin Rouge has almost no plot, so instead of a knockout, this film is two great scenes framing a flatline.
