Recently there has been a proliferation of !votes against candidates who have undergone admin coaching. This is a real shame as Admin Coaching should be something deemed as value added. Unfortunately, for a lot of coaches/coachees coaching is cosmetic. It is also seen by some as a means to how to pass an RfA.
Coaching should teach potential admins how to be better admins/wikipedians. Successful coaching should treat coaching as an extended Editor Review where the coach checks the coachee's edits 2-3 times a month---spending 2-4 hours each time in review. The coach then provides specific examples on how to improve their experience on Wikipedia. Coaching should be seen as a semi-long term process---2-4 months in length. The admin coach shouldn't just give a series of questions and respond to the answers, but should look at the total candidate. What are the candidate's strengths/weaknesses? How can those weaknesses be overcome? The goal of coaching shouldn't be to pass the RfA process, but to improve in general. What areas do the coachees need to work in? The admin coach shouldn't just ask questions, but encourage the coachee to spread their wings and try new areas.
Some take coachees/coaches to get credit for doing so---thus gaming the system. The ideal coachee isn't the one who is ready for an RfA or will be ready in 2-3 weeks, but has an area that needs help--a coachee who has flaws. While they need help, they need to show some sign that they will respond to positive feedback and you have to believe that you can help them. Coachees who are trying to polish their résumé will be seen as gaming the system.
There are two prime types of coaching candidates. First, look for somebody on the Admin Coaching page that could run in 2-4 months with proper guidance, but isn't ready for whatever reason (if they are ready, tell them so). The second place to look are for people who are solid candidates, but need a little fine-tuning---these might be people who failed an RfA. In this case, coaching should be a means to ensure that the candidate does what they were instructed to do in the RfA. It is the duty of an admin coach to dig deeper into the candidate. A lot of times there may be several reasons to object, but people latched onto one and never dug deeper. It is the coach's responsibility to vet the candidate thoroughly so that if there are other reasons, they can be addressed. The admin coach should check their candidate's edits on a routine basis. Check to see if they are doing what the coach told them and are spreading their wings. The coach should not be surprised when they go for RfA.
When coaching somebody, look at their contribution history and help them find areas where they need to grow. If they are a strong vandal fighter, encourage them to get involved with article building. If they are a strong article builder, encourage them to get involved with other Admin-like activities. Try to push them to try new things (not just answer questions). The new things that they try should help them better understand the entirety of the wiki-process in a guided manner with a person willing to help out and provide a critical eye. We don't want people to make "token" appearances in places just to say "I've been there and done that." When coaches do that they create problems. Coachees should make "foot prints" in areas where they have interest. It is more meaningful to a reviewer to see 100 edits on AIV/Help Desk/Village Pump/a particular project than for the coachee to have made five edits each on twenty different pages.
Is it possible that they might venture into new areas on their own? Yes, but a coach can help them spot their strengths/weaknesses. Anybody can learn what is expected to become an admin and can do so on their own. That being said, one can teach themselves how to program a computer. Anybody can, on their own, but that doesn't mean they should. Some people will be able to become power programmers on their own. Some people need a guide. Some people will need to be walked step by step through the programming. Similarly, some people will respond very favorably to coaching while others will not. Some people can benefit tremendously from it, others may be hampered. The question isn't coaching, it is what happens during coaching. Is the coaching personal or simply a series of exercises?
Before nominating a candidate, the coach should do a thorough review of the candidate. Has the candidate done what the coach asked? Are they civil? Do they have edits that demonstrate policy knowledge? Do they have edits that show consensus building? Are they involved in various talk pages? Does the candidate meet the current expectations of the RfA reviewers?