I had two series II GSs without major issue, although I had a couple of central locking actuator issues and a poorly bonded windscreen which caused wind noise that were fixed under warranty.
Whilst still a good car, the series III isn't Toyota's finest hour. It was in the middle of their cost saving drive. The number of faults reported on LOC compared compared to other models, especially considering the small number of GS vehicles actually sold in the UK, is quite high. Hybrids have transmission and battery issues that really aren't seen on other hybrid models, and the petrol ones can have exhaust/brake/suspension issues. Normally the transmissions are fine, but are expensive to put right if there is an issue.