For me, this is by far the most difficult part of piano playing, preparation for performance. I'm a poor performer in general, often shaking and becoming extraordinarily nervous when I go up to play, especially something solo. I've never experienced a true nightmare, but I really don't think I, in my entire life, have ever truly prepared a piece to the standard of excellency required for an even remotely perfect performance. It's never been a big deal before. Usually there are mistakes abound at all my recitals, which don't happen that often anymore. Naturally, if I hear fellow students crash once or twice, something in me just doesn't care if I do likewise.
Really though, this is a major problem for me, because even once one (or maybe it's just me) seems to have a peice "finished", the piece must sort of sit and "simmer". Also, I've found that practicing or maybe, playing it, a lot doesn't help because, in my case, it just reinstates some bad habits that I instilled into the piece when I was learning it. It seems that I, at this point anyway, have yet to acquire the musical maturity necessary for 1. overcoming nerves and 2. more importantly, completely preparing a piece for performance.
For me, piano playing has brought forth no greater obstacle. God knows when and if I'll ever overcome it.
And I plan on majoring in piano performance! Lately I've been giving more and more thought to a double-major...
Edit: I love it when I get lucky on stage though. In fact, I entirely rely on luck that a piece goes well in performance, but I know that the very fact that I do this is probably good indication that my work in unfinished.
Also, in response to the things about different pianos. It does take a certain degree of adjustment for all pianists to play on a different piano. Add a hundred foreign faces to a your already foreign piano on a foreign stage and YIKES!!! My stage fright is so bad, yet somehow I realize how utterly pointless it is.
But yeah, the ability to adjust to different pianos is an acquisition that will come in time. You're gonna have to be playing on a lot of different pianos in your future: impressing friends at parties, performing on stage, going to your piano lesson, playing your Aunt Sally's piano, etc. You'll get the hang of it. It does make it exceptionally difficult though if your practice piano is digital...