WOW. I count at least half a dozen people who deserve facepalms for what they've posted.
Kakashi cannot copy techniques of elements he does not already have. No, the Sharingan can't let him copy elements. Seriously, where do you people get this? He has to already have the elemental chakra in order to copy a given technique.
Here is the fact. Kakashi has 3 elements (4 in the anime) and they are Lightning, Earth, and Water (and Fire in the anime). He doesn't have them because he "copied" them. He has them because he is a high caliber Jounin and like he said, it's not uncommon for Jounins to be able to use more than 1 element.
A ninja typically has an affinity for a particular element. But that element he has an affinity for can "mask" whatever other elemental chakra he has. You train yourself to bring that other element to the surface in order to use it