I spent some little time jerking around with fractal dimension and hurst exponent quite some time ago. I'm afraid I couldn't conclude anything useful out of it. Mostly my results agree with what others report, it's very interesting to follow the theory behind HE & FD, but when it comes to practical application suddenly it becomes very hard or impossible.

Here's another link for you, now that you've expressed interest in this area, lots of good stuff here: http://www.bearcave.com/misl/misl_tech/wavelets/hurst/