I spent HOURS last night installing Mac OS X v10.2 on my G3 Powerbook. I tried to do the upgrade but at varying places during the install everything would stop, a blue screen would appear, followed by a black screen informing me that I needed to restart my computer. It was very frustrating. I read the "Read Me Before Installing" file. I went to the Apple - Mac OS X web site. I checked out the message boards at MacFixIt. It didn't appear that I was doing anything wrong. At one point the installation cranked along for about a half hour, looking like it was going to complete, only to get the blue, black, restart screen.
I finally decided to not upgrade from 10.1.5, but to use the Archive and Install option. This copies your current system into a folder called Previous Systems, and then does a clean install. It takes twice as much disk space and anything you installed into your 10.1 system folder needs to be reinstalled after installing 10.2. This technique worked. It went through the installation, start to finish, with no problems. The installation still takes an incredible amount of time, even if nothing goes wrong. I finished up so late at night, that I only had time to restart the computer and log on to make sure everything looked fine.