For UN ambassador, everyone is going to be focused on who is picked, but an important issue to pay attention to is what relationship the administration establishes for that post. Does that person report to and through the secretary of state, or will that person have cabinet-rank and status (as Holbrooke did). Will it be a Hillary person, so that foreign policy is unified under her control, or for some issues might it be a competing power center?
Rice is definitely not a Hillary person, that much is clear. But another interesting question is what posture Obama will adopt towards the UN generally. As I noted earlier today, the Clintonites never saw Turtle Bay as the ultimate arbiter of anything. And while some liberals may now celebrate the UN as a noble corrective to obnoxious Bush unilateralism, there's nothing very liberal about Chinese and Russian veto power in the Security Council. (See Darfur, neverending horror in.)
Come to think, perhaps this new "change" moment would be a useful one for Tony Blair--ideally with the support of Obama and Rice--to renew his call for UN reform, something that could include Security Council seats for nations like Germany and India, and/or ones from Latin America and Africa. Such questions are actually what McCain's "League of Democracies" idea was trying to get at.
Update: Another reader who knows whereof he speaks adds of Rice
In some ways, this feels like an exile for her to NYC -- Dep Sec at State or Dep NSC would have placed her much closer to the action. Instead, I see this move as setting her up for NSC Advisor or even Hillary's successor in the second term.