A poll regarding the thread at http://priuschat.com/threads/2012-prius-c-low-speed-cold-start-vibration.141833/#ixzz3EkGQ43Tb "After a cold soak, the gas engine starts, but its very shaky, almost like a miss-fire. And at about 10-20mph when you go to accelerate lightly, to make the gas engine start, it starts vibrating again. but if you give it more gas, it smoothens out. Still sounds like a misfire to me..."
Your poll is incomplete, for a couple of reasons. First, virtually EVERY car on the road gets "cold soaked" at least once a week when it sits unused for 24 hours. Secondly, my situation is not listed; that is, when the engine is cold SOMETIMES I notice a slight vibration but most of the time there is none. Being in Florida where it never gets REALLY cold might be a factor.