Step 7: Troubleshooting
The main problems you're likely to encounter are getting Processing and the arduino to talk to each other. Make sure you install the arduino software - this will bring with it all the necessary serial libraries. You can find avoid problems with the circuit by testing as you go - test each LED, then each strand, then each transistor set. If all else fails go back to this to diagnose where the problem lies.
Now that I've managed to squash all the bugs from my own setup, I can't think of what they were off the top of my head. Post any problems you have, as I probably ran into them and have since forgotten.