The music attached to a film creates the environment, I believe, moreso than the literal environment depicted through the visuals…
The film is a strange one – almost dreamlike in its ‘world’ with Mel Gibson as the outsider to the surrealist hotel that is the Million Dollar Hotel. But the soundtrack really complements this context with soft, slow, soothing guitar riffs and chords. Echoes litter the album but the two stand out tracks are by U2 – ‘Stateless’ and ‘The Ground Beneath her Feet’. The latter is on the album All That You Can’t Leave Behind (albeit as a bonus track), but the former is only available on this soundtrack. The third track I have chosen is Milla Jovovich singing Lou Reed’s ‘Satellite of Love’ showing the ‘dream like’ quality of the film… until the track descends into a strange territory. I always wish the song ended after 3 minutes, because the wailing ruins the song completely. In some ways, this song is not too far from the film itself – in that, as good as the film can appear and look, there is something uneven and strange about it making the film a little bit too strange to comfortably enjoy.
1. The Ground Beneath Her Feet
3. Stateless
simoncolumb.com 
I used to have this CD back in the day, but I must have sold it off at some point when I realized I was only keeping it for two tracks.
That said, “Ground Beneath Her Feet” makes my list of my 20 favorite U2 tracks. Such a glorious song!
Yeah, there are few dud tracks on the album, but I think STATELESS is pretty amazing and, again, the dream-like element is something great to chill out to. As a completist U2 fan, I have to keep it!
Didn't Bono write the movie too. I really hated the movie, in that special way I hate just about all Wim Wenders movies that arn't Paris Texas or Wings of Desire but I should maybe check out the soundtrack since it gets such high points from you and hatter.