I think what happens normally is that the big screen shows foul play, then the crowd start yelling, then the ref looks up at the big screen and then makes the decision to go to the TMO or not. After that though I don't think that the crowd gets the decision it's up to the ref/TMO. Look at Ulster v Saracens with Payne's red card, that was for the home team in a massive game. As is said before the TMO can't hear the crowd, he shouldn't be swayed.
THIS^^^
Its the decision to actually go to the TMO that is being influenced, not so much the subsequent decisions.
If you are the referee and you suddenly hear raucous booing while a replay is being shown, it would be hard to resist looking at the big screen to see what they are booing at, espocually if it is happening during "down time" while a player is being treated for injury or a substitution/replacement is being made.
As SelimNiai said, the perception that the referee is influenced is not a good thing either.
we should just do away with the TMO for good.
we have citing for foul play, and then no more moaning from anyone.
The Genie is out of the bottle, and there is no putting it back I can't see it ever happening. In the "old" days television video was poor resolution and poor quality. We didn't pick up the large number of mistakes that were made by referees at vital times that cost teams matches. Not so now; video is HD 1920 x1080 pixel resolution; photographically crystal clear. Mistakes become obvious. It simply makes no sense to have millions of people at home able to see clearly while we blindfold and hamstring the referee.
I have a collection of older matches going back 30+ years and they are replete with what we would now call refereeing blunders that would almost certainly have been turned over by the TMO.
Take for example....
1. the 1987 RWC Semi final between Australia and France. There is no way on God's green earth that Serge Blanco's last gasp try in the corner would have stood had there been a TMO. He was in touch before he grounded it. Even if you could somehow argue that it was inconclusive, two passes earlier, Rodriguez knocked the ball on picking it up. With a TMO, the 1987 final would have been New Zealand v Australia.
http://www.youtube.com/watch?v=JnzNxVpAXQw
2. the 1973 All Black Tour of Great Britain and France. Tom Grace's last gasp try for Ireland against NZ would certainly have gone to the TMO. The referee was 15m behind the play and directly behind Grace as he grounded a loose ball close to the dead ball line. There is no way he could have seen the try scored from his position. The ball looked like it crossed the dead ball line before being grounded, so the question would have been "try or no try?". The TMO would have to see a grounding in-goal, and this is simply not visible, so that try would probably have been ruled out.
http://www.youtube.com/watch?v=wXjDn6l6M74