I can't really compare an American using "spaz" to anyone using the word "idiot". For generations, at least as a noun, it meant nothing other than a derogatory way to refer to the mentally handicapped. I don't think we've referred to people in the US who had any disability as "spastic" for a long time, and I suspect those who associate it with CP or mental handicap might either have grown up in an area with British (or maybe Canadian?) influence or where people hung onto the old ways the word was used (if it was ever used much in the US to mean someone with CP or someone with mental retardation at all). When/where I grew up, it meant clumsy and scattered. When someone uses "idiot" as an insult, light or otherwise, however, it is will the full understanding of the meaning in their own dialect.
On a sort of related note of word origins, at one time "moron", "imbecile", and "idiot" were all medical terms to describe mentally handicapped people by degree of disability. I remember being shocked finding this out by reading old medical books. "Hysterical" means a wandering uterus because it was theorised during ancient times that women got upset because their womb would detach and move about their bodies causing them to lose control. I know there are more, but I can't remember them off the top of my head.