Re: Speed in waza?
I remember Sugano Sensei saying once in a seminar that we should sometimes practice slowly and other times quickly. Then he did a couple of techniques where he told us specifically, to do this one as precisely and correctly as we can, and then the next technique he had us do it FAST, and then just get up and attack again quickly.
I still remember that class and in my own practice I've found that idea useful. I think practicing slowly (or at least, as slowly as you need to do your best) is how you learn to get it right, but occasionally practicing quickly has merits too, even if you do get sloppy. For me I feel like it kind of shows you 'where you're at', and pushes your reflexes in a different way than slow practice does.