I'm using 10.2.8 on a 1.25 GHz PB G4 (1 GB RAM). I noticed the same thing on the original 1 GHz 15" PB G4 (768 MB RAM).
Usually after waking from sleep, launching applications can take a very long time. As they are launching they bounce many more times in the Dock than they ususally do then quit bouncing for a while, and finally do come up properly.
Any idea what might be the problem?
Dominik Hoffmann