I had the same problem as You Am I describes at the beginning of this thread. I thought it weird that the DVD passed the verification, yet the 'basesystem' package could not be verified. Anyway, I took my mail order copy of Leopard to the store, and they exchanged it, no questions asked. I tried the new install DVD and had the same problem. I had been having strange problems with Tiger over the past 2-3 weeks (programs would not start, or would crash for no reason, etc.), so I then wondered if it was a hardware issue. Turns out it was. I ran the Apple Hardware Test, and found that I had a bad memory stick (Error: 4MEM/4/40000000: 1e156bc8). To narrow down which stick it was, I took one out, to see if the error kept happening. Turned out it was the aftermarket memory I installed about 6 months ago. I put the original factory memory back in it, and things are going better. Leopard is 80% installed.
So for those of you having the problem, you may want to try the Apple Hardware Test just for kicks. It may be on the Leopard DVD, but I ran it off the DVD that came with the MacBook. Instructions for running the test are on the Apple Support site here:
http://docs.info.apple.com/article.html?artnum=303081
Good luck.