Here's a fairly obvious starter list that we'd like to see in a nominee (let's set aside the attribute many of us especially want, which is a willingness to decide cases the way we think they should be decided, since it's hard to come up with a real consensus about how that is to be implemented):
Willingness to consider the possibility that one is wrong.
Ability to work effectively on a multi-member Court.
Ability to set aside one's personal annoyance with or hostility to particular colleagues, lawyers, or litigants, even when the annoyance or hostility is justified.
Understanding of the world and of the likely practical effects of various legal rules.
Clarity and precision of thinking, and ability to write clearly and effectively (or to edit subordinates' work well).
Creativity in thinking up (within the permissible legal boundaries) solutions that accomplish the goals that one is (properly) trying to accomplish, for instance in crafting a common-law rule, or an interpretation of a statute that's consistent with the text yet likely to accomplish the statutory goals.
Willingness to subordinate one's views to the legal commands. (I recognize that there may well be disagreement about the terms of those legal commands -- for instance, how important text or original meaning may be -- but I think most observers would agree that once a judge concludes that some legal rule is binding, the he should comply with it even if he doesn't like the result.)
Willingness to work hard.
Ability to work efficiently.
Good judgment in what to delegate to subordinates.
I'm sure there are other items, both obvious and nonobvious, that I missed.
But my point here isn't really to look for an exhaustive list, or to rank the items. Rather, it's to ask a few related questions: If we come up with a fairly well-understood list, how do we judge nominees -- and of course right now we're talking about Harriet Miers -- against it? If the President's explanation for selecting someone he knows very well is that he has a much better sense of how she fares in these categories than he would about a stranger (even an illustrious stranger), should we be impressed by this explanation or dismiss it? Are some of these attributes more important than they at first appear to many, and others less important?