Well, it really doesn't make sense
Mind you I have seen this innumerable times and the thing that I have noticed is that every time you watch it, WHILE you watch it you will keep going (over and over) "Oh! Now I get it!" At least until you come to the end of the film and try and put the whole thing back together. That is when it becomes like nailing Jello to the wall. It's just kind of a mess.
Mind you, I absolutely love this film though. I give it a 9 and will watch it repeatedly because it almost always seems like a different film.
Another film that I find has this same effect is the original DOA. Seems to make sense until it ends, but then you really can't quite put all the pieces back together. Another excellent film. And this one practically defines 'noir'.
The Big Sleep comes close to the same effect, but it is just difficult, not impossible, to put back together. (helps that the book makes sense)
And yes, the theme song at the end is really catchy. And also, this would be an interesting experience on LSD.