Rasengan is not really a jutsu. It is simply a form of chakra manipulation and thus can't be copied. Naruto's kage bunshin can definitly be copied since it requires seals to perform the jutsu. Rasengan doesn't require hand seals and even if it did it couldn't be copied.

Sharingan can't copy all types of non-bloodline techniques. Just consider summoning for example. It does require hand seals but it requires a contract with the summoned animal and therefore sharingan is useless against summoning.