What would happen to somebody voting in opposition to a proposition at LDS General Conference? I'm watching the semi-annual LDS General Conference. One segment just went by that was some general business of voting to retain people in various roles or assign new ones. Several thousand people are present and voting.

The camera work going into the live broadcast was hard to see, but it looked like the entire audience voted on every issue instantly and unanimously. Having watched and participated in many similar events both secular and in various Christian traditions, this seems inconsistent with what inevitably crops up: human nature seems to dictate that given enough people, there is always some sub-set of nay-sayers.

What do these votes represent? Have these issues been vetted some other way first? What procedure would be followed in the event of some opposition votes? Is it an issue of needing a majority? What personal experiences would somebody expect if they were to vote against an issue like retaining a prophet or one of the other major leadership roles in the LDS church?
This originates from a revelation given to Joseph Smith, recorded in Doctrine and Covenants 26, and is known as the law of common consent. Note that this is different from congregationalism in that in common consent, a decision is already made through prayer and by inspiration, and the decisions are not made by democratic voting, per-se. Those affected by the decision or change then sustain it, not necessarily vote on what should or should not be.

Sustaining leaders is a regular occurrence in the church, even in local meetings. Raising the right hand may be understood, in some way, as a pledge or covenant to help and support whoever is being proposed.

If somebody opposes, it is generally done because of some first-hand knowledge the opposer has of the person in question. In local settings, that person will be asked why after the meeting (usually the reason must be for some grave sin, or unworthiness to serve in the position, which leaders usually know about anyway as they may help the person through the repentance process).

In general conference, there are about 21,000 people in a single session in the Conference Center. The conducting authority will generally conclude with "Insofar as I have been able to observe, the voting in the conference center has been unanimous in the affirmative."

If there is an opposition in general conference, the person is directed to speak with their stake president who takes the matter, if it merits attention, to higher authorities.

Update: I was in attendance when this happened today, on Saturday, April 4, 2015, during the afternoon session of General Conference. Some attendees opposed and the speaker simply remarked, "Thank you, the vote has been noted." Instead of saying that voting was unanimous at the end, he said, "The voting has been noted. We invite those who opposed any of the proposals to contact their stake presidents." [Video]