I think that Dancer In the Dark looks at the Hollywood-isation of culture, through the musical segment of the film, intentionaly bad diologue and as a theme that runs through all other parts of the story. It then ends up critasising Hollywoodisation by attaching it to Bjork's death. So there's a huge irony in the fact that Bjork is the only non-American character in the film. It's almost as if Von Trier thinks of Hollywood as a virus that spreads to all corners of the globe.
Most of Bjork's actions in the film can be linked to Hollywood. At the end of the film she sacrafices her life to save her son's sight, just like Humpfrey Bogard at the end of Casablanca of Michael Bein in The Terminator, both of home make sacrafices to save the people they love. It seems that Von Trier is synical towards this sort of martordom and suggests that Bjork, although victimised, is still responsible for the film's tragedy. It's as if her decision to give away her life was inspired by the movies.
The film also suggests a method for the improvement of Hollywood, saying that it needs to have a grasp on reality by contrasting the dogme-esque style of the main part of the film with the audacity of the musical numbers.
So anyway, try and ignor my previous comments on Dancer In the Dark as they were written at a time when I didn't have a clue what it was about. Dancer In the Dark is NOT pro-musical.