I find it funny people say "Sharingan can copy handseals, but not Rasengan".
Why not? Ninjutsu = not handseals. Sure, the handseals are needed as part of the Jutsu but in the end its chakra manipulation thats needed to perform the actual Jutsu. (if it was just handseals then Lee should be able to do it but he obviously can't.)
So basically I think if the Sharingan user has the necessary chakra control then he should be able to copy Rasengan, I seriously don't see why he shouldn't be able to, it has special requirement.
I think Sharingan can copy pretty much anything that doesn't require alterations to their body, special blood, a scroll to be signed or any other physical thing they don't have so long as they have the skill to do the technique.