It's a fairly meaningless term, really.
Like a lot of descriptive terms, it's been cheapened through overuse. I once heard Brian Wilson (of Beach Boys fame) described as a "genius." The man's a talented musician, but a genius? What was Beethoven -- chopped liver?
Yeah, the dilution I think is a part of it, but it's always been a pretty flimsy term. I've got a bit of time, so I'm just sort of thinking out loud here...typing out loud? Typing as I think, I guess...
Intelligence is reliant on so many things, circumstance being one of the greatest, and the one everyone forgets about. We all want to attribute all our positive aspects to something internal and innate, but that's only part of the picture. One has to wonder, how would Beethoven's genius have presented itself if he were born in the stone age. How would Brian Wilson's "genius" have presented itself if he were born in the 18th century and classically trained from infancy?
Some people rely on IQ to give an objective measure of genius, but that's just stupid. IQ tests are flawed and biased, so much so that results can vary greatly for the individual being tested depending upon the test and when and how it's given. I've personally administered a battery of tests to a learning disabled individual who scored 65 on one (technically moderately mentally retarded) and 145 on another (technically well into "genius" range). IQ can tell us a bit about people's intelligence, but not a lot.
It could be more meaningful to define genius based on product, not on capability. Einstein was quoted above, and Dumbledor also provided wise words on the issue: "It is our actions, not our abilities, that make us who we are."

Is someone with a 145 IQ a genius because she tests well? What if she never produces an innovative thought? Is someone with a 100 IQ average even if their work or ideas are consistently innovative? I don't think a lower IQ precludes ability for innovation.
So, is genius the production a paradigm-shifting innovation, either physical or conceptual? Perhaps. By that definition you could, reasonably, call "Pet Sounds" a work of genius, and maybe it is. Or maybe it should be about quantity of output as much as quality, which would eliminate the "cheapening." On the other hand, it's been demonstrated that most "geniuses" produce their paradigm-shifting ideas only once and usually in their 20s to early 30s.
I guess the question is, is genius aptitude or action?