hi!
Have you made a simple spectrum/waveform visualization using computeSpectrum?
From there, try adding interesting combinations of effects. A blur every frame, scroll every frame, etc. Cool stuff will happen!
For beat detection in particular, a very simple method is to sum all the values from computeSpectrum, and if they are over some threshold, you have a beat. It doesn't work toooo well, but it's a starting point.
Here are some more ideas to go from there:
http://www.gamedev.net/reference/program ming/features/beatdetection/
Using this way, you keep a running average of the 'energy' of the sound to compare your current energy to -- so that makes the algorithm a little more dynamic.
Keep in mind that beat detection is *tough*, especially real-time. computeSpectrum is pretty limited in what it can do, but unfortunately we are stuck with it until Flash 10 :)