You could use a chart that the student keeps themselves to help them track their own behaviors. As they notice a classmate doing an "unexpected" behavior, they can check their chart to see if they have done that as well.

I would pull the student aside to ask him if he thinks the behavior he demonstrates is distracting. When doing so, don't say that he is the one doing them, just say "you are good at pointing out distracting behavior, would it be distracting if you do X?" and if he agrees to them, politely point out that he sometimes engages in the same behavior. If he has the desire to correct others, he likely will want to correct his own behavior as well.

This student should use self monitoring strategies for his behaviors. When he notices he is doing an unwanted behavior, he will learn how to self correct.

I think that the student is well-meaning at heart, however, this can be an issue when dealing with students. What I was thinking is if you could have a sit down and communicate with the student and keep the classroom transparent, then that may be of service. The issue may be worthwhile in bringing up to the student's parents, as well.

Have the student Keep a log of the unexpected behaviors he does and work out ways to correct them and prevent them from happening again.

Probably have a conversation with him or his parents to update his behavior on it. Maybe they know some pointers that you don't since they live with him everyday.

I would pull this student aside to point out that his behavior is now the very same behavior he criticizes others for. Ask him why he thinks its appropriate for him, but not others. Some students may be reasoned with in this way.