Actually every sharingan user can copy/remember the jutsu, the movements, the fighting style of their opponent... and it is not such a big thing to show it every time they do it...
And also remember... just because you know how to do a jutsu, it doesn't automatically mean that you can use it... if your body is not prepared, and trained for that kind of technique... then you won't be able to do it....
And the sharingan can copy jutsu that involves seals... i mean you can not copy the rasengan, rasenshuriken for example...