If you are presenting to management, learn this lesson. As a consultant, I do a lot of presentations, and attend a lot of meetings where other people present. Rands provides the best advice: if someone hits you with a surprise, acknowledge the concern, admit you don't know the answer, and offer a plan for coming up with the answer. Sometimes one of the players (and not necessarily the person who brought it up) will try to leverage the outstanding issue to delay a decision (or drive the decision the "wrong" way). Knowing in advance that a "screw-me" may come up, and being prepared to handle it, will help you deal with this situation. You may be able to get agreement that the issue is not material to the decision, or you may be able to get a provisional decision pending an answer to the open question. What you want to avoid is losing another week while you research, communicate, and reschedule the meeting.
I've only recently (thanks to Rands) discovered the value of meeting with key stakeholders prior to meetings to hear their concerns, state my case, and insure there are no surprises at the formal meeting. Most of my meetings are becoming quick rubber stamp affairs! Soon I'll either be working on more complex projects or I'll be able to get things done without having formal meetings at all.
Many to many meetings are often a huge waste of time and a poor way to get things done. The fact you're going retail to the individual people also gives you a LOT more influence than you would in the large meeting.
It seems like more work, but due to its high levels of relative effectiveness, it is so much less work because it works so much more often.
Getting input/feedback from key stakeholders before the meeting is a great idea. Unfortunately, you will occasionally run into people who either "don't have time" to review materials before a meeting, or who deliberately hold something back to use against you in the meeting (you'll also run into people who say they've reviewed stuff in advance, but then suddenly "realize" something in the meeting). Establishing the ground rules in advance (so that everyone knows that stakeholders had time to review the materials) can help - sometimes people are reluctant to admit that they didn't review in advance. Unfortunately, there's no sure way to avoid a surprise, and sometimes people legitimately identify a concern during the meeting. When that happens, the key thing is to make sure that there is a clear action plan for dealing with the issue. You want to make sure that people walk out of the room knowing how the issue/question is being resolved, and what the deadline is. If not, you will probably find that you have to have the meeting all over again.
It's things like this that make me remember why I only work in smaller businesses these days. Ah, no politics, other than the usual wrangling with clients.