Sure, and that's why it works. Much like a typical story presents things in the future that change the story, this movie changes things in the past. However, when you step back and look at the whole story from the other side, the tale itself is still interesting even once you've put all of the pieces together. Or at least that's my feeling.

[spoilers]
Viewing it forward would have been a completely different take on the movie- rather than having Leonard’s perspective we'd get everyone else's, but we'd still get to see the manipulations and lies. I completely missed how Teddy was so obsessed with the car the first time around, and knowing that Natalie is using Leonard ahead of time might change the way we perceive the scenes with the two of them, but it is still fascinating story telling to see how she behaves in different ways around him depending on what she's trying to accomplish.
[/spoilers]

Incidentally, apparently there is an Easter egg on the two disc version of DVD that lets you view the movie in reverse order (or chronological order). My wife bought me the first DVD when it came out, so I've never really had a chance to try it out. Not sure that I'd want to sit around for two hours watching the movie that way, but it'd be interesting to see how it comes off without the "gimmick".