I was going to call this post "The Downsides of Privates" but I think "5 a.m." says it all in a nutshell.
I would have to say that the early morning start is my number 1 least favorite thing about private lessons, and I'm a morning person. But getting up in the wee hours, sitting around in your pjs with a cuppa is a very different thing from getting dressed, going out in the freezing cold air to the freezing cold ice rink.
Flippancy aside, private lessons do have their problems. Scheduling. Cost. Go back and read "how to choose a figure skating coach" (parts 1 and 2). Follow that advice and many problems will never manifest.
Some of the less tangible downsides to privates involve interpersonal relationships. Coaches and parents can get jealous of the skater's relationship to the other, as can siblings. If one of a coach's students is more successful than another, resentment can flair, and I'm not talking about the skaters, I'm talking about the parents. Remember to leave competitiveness at the competition. Training is about personal best, and furthermore has little or nothing to do with the parent. Being jealous of the coach, the other skaters, the other parents, and/or the other coaches is pointless.
Going into this, I thought the downsides post was going to be easier to write than the upsides one, but it's not. A lot of the problems in coaching relationships are terribly specific to circumstance. It's an "everything you need to know you learned in kindergarten" sort of thing. If you follow good general practices about paying on time, knowing what you're paying for, showing up at lessons and working hard (both coach and student), avoiding gossip where possible, you will nip the downsides in the bud.