Re: ineffective technique from sensei?
Henka means 'change' so henka waza is 'changing technique.' Generally this is taught, as Brian said, as transitions between techniques. Nage starts doing ikkyo, say, and switches to something else, kotegaeshi perhaps, mid-stream. Learning how to do those transitions is critical, IMO, to developing smoothness, seeing the relationship between the various techniques, and to respond correctly if uke changes their game or finds an opening.
When I am teaching I generally don't mind if a student points out (politely, without breaking my nose :-)) an opening or doesn't fall if I don't have their balance, etc. Often I will leave an opening deliberately to demonstrate what to do when the technique isn't going well, but sometimes I just mess up. That's all right - we all do. I think it's important for my students to learn the sensitivity to tell when things are going well or not, and how to correct any problems as they are happening. That's much better than just stopping, resetting, and starting again.
Usually those corrections start with fixing posture but sometimes it involves switching to another technique (henka waza). In many classes when we do basic practice, we are applying a specific technique to one attack. That's a very artificial situation. O'Sensei said that ultimately there is no technique, only correct movement.