The first instance that comes to mind wasn't even in a science fiction novel, I don't think, but serves as a shining example of bad science in literature. You know you're in trouble with the science when the archaeologist (who would very well know better or they should rescind his Ph.D.) comes along and proposes dating some rocks using the Carbon-14 method.
I can't recall the name or author of the book...this happened in the first thirty pages or so, upon which I threw the book across the room in disgust and got it back to the library as soon as I could get the hideous thing out of my house.