Kakashi says he completes the jutsu as soon as obito gives him the sharingan and he is fighting all those stone ninja. i don't think an imperfected jutsu is the cause.I think Kakashi killing Rin was a complete accident through use of an imperfect/incompleted jutsu. When Obito sees Rin with all the black fuzzy around her I think he is seeing from Kakashi's point of view. We know the speed required to use the chidori causes tunnel/blurry vision so I think Kakashi used the Chidori before he could fully master it and hit Rin with it by accident.
and if kakashi had killed rin with chidori/raikiri/whatever it was or is called, he probably never would have used it again