What results when easily-herded people gather to protest an issue that is not clearly understood by them. They make unintelligent, or just plain non-sensical "arguments". In a dumbonstration you can see people holding up signs as illogical as "Don't Kill Grandma," or "Get Your Gov't Hands OFF my Medi-Care."
Dumbonstrations are usually, but not always, results of lobbyists or companies with significant interest to push. These vested interests begin an astroturf effort, and recruit people who don't think critically about the issues. Consequently, what should have been a one-voiced demonstration of opposition to a clearly-defined topic devolves into a series of random rants and rambling with no sense of cohesion. Hence, you get comments that vary from the politically incorrect to the downright racist– reflecting the attitudes of the people that comprise the dumbonstration.
A certain non-news TV personalty is encouraging people to gather for what he calls "Tea Bag Protests." These usually devolve into a large, muddled dumbonstration.