andrewbmoore — I have also had a few rough ICE starts and rough ICE stops (but not many). I think that the occasional shaking when stopping the ICE is a consequence of Toyota's "ICE-stop" strategy occasionally not working as intended. Their patents discuss how to stop the ICE without significant engine vibration. The occasional shaking when starting a cold ICE might also be a failure of their algorithm; i.e., a programming error. MG1 is involved in this strategy, and it is possible (as you suggest) that it is occasionally holding the ICE's rpm too low while the ICE is still receiving fuel and spark. Other possible reasons also occur to me. For example, the fuel injector and spark control algorithms might contain a programming error that sometimes rears its ugly head. It's difficult to say why this sometimes happens.

Stan