Re: Kotegaishi weakness?
I think that within any style or association you can talk in a shorthand that outsiders will find relatively opaque; but I'm not convinced there is as much difference in the concepts as there is in the vocabulary. A couple of times at Aikikai seminars I've had the pleasing experience of hearing a completely unfamiliar and baffling explanation, and then trying the demonstrated technique and having it click into place as an expression of something I do know.
The people who have thrown me with kotagaeshi, though, have made a clear difference from koteoroshi--they don't let me fall backwards out of the throw, but force me to go forwards over my arm. (I need to learn how to do that properly before someone breaks my wrist.)
One way to learn the unbalancing form of these throws would be to deliberately hold uke's forearm rather than his wrist. Now the wrist control is out of the question, but the unbalancing can still work. Knowing how to do this gives you a fallback if you miss uke's wrist--especially a problem for me if there's a big weapon being waved around.
I used to think koteoroshi was purely an unbalancing throw--that we'd softened it to the point of losing the wrist control completely--but I expressed this view to one of our yudansha, and got the usual sort of learning experience.