I have a 2008 Prius Touring model and experienced the above symptoms after having not driven the car for about 6 weeks. It started acting up after I backed out of the garage and while in reverse and my foot on the brake pedal. It shook quite a bit for about 15 seconds and then stopped and seemed to drive normally. I drove about 3/4 of a mile and entered a parking lot to park and while in drive it started shaking and making noise for a few seconds and then it quit and ran normally and has since then. I also had a hard time trying to get the remote to activate the door locks but eventually suceeded. The one other odd thing that happened was that the morning after the above incident, I went to start the car and a light on the dash came on showing an outline of a key and the car wouldn't start. I then used another remote and the car started fine. I realized the battery in the one remote was dead and have changed it. What I was wondering was whether the failing remote battery was the cause of the shaking, chattering,slipping noise from the transmission? I'm due for a transmission fluid change and will do it soon.
You didnt drive the car for 6 weeks? Your 12v battery was/is low in voltage confusing all of the computers because they need reliable 12v to run. I'd start by searching the site on how to check the 12v voltage via the MFD.
This is beginning to sound like the "just reboot it" response to problems with Microsoft Windows... I bet it won't be long before we get this same response to "my tire pressure is low" and "my car is out of gas"...