I work with kids (ages 13-21) with mental disabilities. Some know, some don't seem to know.
It seems like it depends on the severity of the disability. The ones with the most severe disabilities probably don't know. Or, they know they're different, but it's not really an issue because they can't talk or function on their own, or perceive enough of the outside world to know.
Some do know, however. The ones that are most functional seem to have the best grasp of this. They know why I can drive a car and they can't, even though I'm only one year older. They know why their parents have to help them with lots of stuff. I'd agree with what Amanda said about frustration for this scenario.
Some use that knowledge to their advantage, and some don't care about it at all. Someone with Autism (and a good deal of people with autism also have mental retardation of some form) probably wouldn't know or care that they are different. There is a theory that some people with autism only understand the existence of their own perspective. So, I'd say it depends on the person and the situation.
If the question was "Do these people know their limitations?" I would think that's a good question for any person, not just the disabled.