Re: What is the correct hand placement when do kote gaeshi?
The correct grip is the grip that sensei demonstrates. From there, you have the best opportunity to feel the joint manipulation, which in my opinion, is quite varied in the kotegaeshi kata. Seminars are a great opportunity to see variety and get hands-on.
From an instructional perspective, I have taught kotegaeshi as a corner drop (sumi otoshi) with a wrist control (kote gaeshi). We have a few rules:
1. The wrist twist should apply sufficient torsion to prevent uke from turning into nage and you should apply torsion upon gaining the wrist.
2. Any lateral movement should maintain the center of the technique.
3. The bulk of the throw is committed through the corner drop, not twisting wrist (the twisting is just to maintain the torsion in unity with the body movement)
I made these rules because, my opinion, the most common kata failures are:
1. Nage waits until the end of the technique to twist uke's wrist to make them fall down.
2. In stepping, nage loses the "center" of the technique and creates a mutual orbit for both partners.
3. Nage envisions the fruition of the technique is derived from the joint manipulation (and over-focuses on the wrist).
To Cliff's point, I am fond of using the forearm because it relieves the pressure of ukemi for students who are not comfortable with wrist-twisting and it requires the kata to work absent joint manipulation. Also, there is a segment of the training population that reinforces how stupid it is to try twisting a wrist on a participant who is less-than-willing.