It's been stated that Christian appeared,"only while Jack was under."

Well, Jack tried awfully hard NOT to be under during his appendectomy. Did he have that (preventing his father from appearing?) as an ulterior motive?

Would that be common in any way... (or possible) for a patient to be as awake as Jack wanted to be during his surgery?

Of course, prevailing forces managed to get Jack knocked out...

So Christian could appear...?

How would Jack know to try not to be unconscious in order to stop Christan from appearing?

In the future, Christan appears to Jack when he is conscious and sober, so his abilities don't appear to be limited to Jack's state of mind.

I really want Jack and Claire to find out that they are brother and sister.
Cool parallel that they both saw CS at nearly the same point in the episode.

Jack was awfully insistent about Kate holding up a mirror during the procedure. They could only get him under after she and that mirror left the O.R.