I have a direct who is on a performance coaching plan because of poor performance. One of the actions that I am responsible for is to conduct random outbound calls to the directs' customers (I work in a customer centric workplace). I do this to gauge the customer's response on how well the direct is handling the customer's needs. My direct knows that I do this and I share the customer's feedback with my direct. Now, my boss wants to get in on the action and also wants to do the same thing. Although he won't share the feedback directly with my direct (he will pass it off to me to provide feedback to my direct), I'm not comfortable with this.
What are your thoughts on this? Could having the added pressure of both of us making these calls help or hinder my direct? My direct has recently moved away from the formal performance coaching plan because there has been improvement.

It's fine
If your boss wants to, you have no choice but to let him.
I don't know why he thinks it would add value, and the fact that things are improving would seem to me to suggest that your boss's involvement is even less valuable.
My sinister side suggests that maybe your boss doesn't like this guy and wants some proof...but that's just a wild guess.
Let him, and be nice about it.
Mark
Thanks for the input.
Thanks for the input. I'll be nice....; )
Nothing you can do about it
If your boss wants to make the calls there is nothing you can really do about it. I would not spend the time or energy trying to persuade your boss otherwise. I agree with Mark that your boss may not like this employee and is looking for evidence to help him or her out the door. Also, could it be that your boss is not happy with the way you have handled the situation? Depending on your relationship with your boss I might ask him if and how you could handle the situation better. It might be a teachable moment for you.