They're fractious, frequently wrong, and have lost much of the public's faith. But their insights are still valuable -- as long as you don't expect them to predict the future.
Imagine you are the Royal Physician in England some time during the 14th century. The prince is sick, and you've been summoned to help. You call in two experts for advice. The first says: "Use leeches to suck out the evil humors." The second says "No, you must bleed him to get the evil humors out." They start to argue, insulting each other in nasty epistles. "Leech guy is secretly working for the French!" alleges Bleeding Guy. "Bleeding Guy just wants the prince to die because the prince wanted higher taxes on the nobles!" Leech Guy fires back.
What's the right move? Well, in an ideal world, you would go and get 999 patients who have illnesses similar to the prince's and give them all a variety of household substances, such as bread mold. Then you would take careful note of who died and use statistical analysis to figure out which household substances cured disease. Thus, you would discover penicillin and invent modern medicine.
For the rest of the story: http://www.theatlantic.com/business/archive/2013/06/should-we-trust-economists/276497/