It's remarkably easy to do in Audition's multitrack mode. Well, the technical process is, although the judgements about where to do it aren't, sometimes, if you want the results to be really inaudible. And yes, it is a pretty normal process in classical editing. What you need to do is look for a tutorial about crossfades, because this is how it's done. Crossfades can be any length you want them to be - if you really want to cut into a fraction of a note, even, you can do it relatively easily.
In the middle of the tutorial you find here you will find the basic information about crossfading. With classical stuff, the crossfades tend to be relatively short, but there's no limitation on where you place them, really. There is one thing you need to be careful about in audio terms though, and that's the room ambience. Because of the reverberation of the room your piano is in, just re-recording a faulty without playing into it can sometimes make it sound rather strange, if the join loses previous reverb. Admittedly this isn't normally much of an issue with pianos, but it can still happen. It can be a bit of a pain with recordings made in large acoustics though, and you always have to record re-takes taking account of it.
One day, when I have a bit more time, I'll do a tutorial about classical editing specifically. But it's going to have to wait for a while whilst I actually do some...
Thank you Steve. that tutorial was super helpful and I already tried it out to fix a mistake and it worked. If I really focus, I can probably make the transition unnoticable.
Now that I know the key word - Cross fading, I will be digesting many tutorials on the subject!