Public opinion is the weak point in many systems that are supposed to converge to an optimal socially-beneficial equilibrium.
The way competition and free markets are supposed to work, someone else would've introduced ethanol as an anti-knock additive, sold gasoline cheaper (and healthier!), and everyone would've benefitted. But Kettering & Midgley went on an extensive PR campaign after their invention to convince the public leaded gasoline was safe, and they had GM and Dupont's full advertising budgets at their disposal. The public wouldn't know any better, so they believe what they're told and leaded gasoline becomes the standard.
You can hear echoes of that with many Facebook advertising & misinformation campaigns today.
This also causes stock market bubbles & crashes. People are supposed to independently value securities, and then their errors cancel out and you get a very good statistical approximation of true value. Instead, they invest in what everyone else invests in in, until prices have been bid up to insane levels, then run out of gullible buyers and the price crashes.
And brand-based monopoly. Instead of judging product quality for themselves, they buy products that all their friends are buying, "trusted brands", and this creates a barrier to entry that new entrants have a very hard time surmounting.
Democracy is affected too. In theory, the best candidate should win. In practice, the candidate with the most money to buy ads wins. People's opinions are mutable; they don't rationally seek out information independently and make an informed, self-interested choice. They tend to trust what they hear a lot, which creates a market for influencing people's opinions.
I can't think of a way to solve this, though. The "solution" would be to go from a high-trust society to a low-trust society, where everybody basically assumes that whatever they're told is a lie and ignores it. Societies like this have much higher transaction costs, much lower rates of innovation, and much higher rates of violence, which is not an improvement.