Arguably, the problem with the Assembly was that they'd vote for whoever spoke the most convincingly, as opposed to who had the best argument. This wasn't much of an issue when Pericles was around, as he tended to be quite intelligent, but after his death the Sophists made their money by teaching people how to speak well (but not how to think well, as some of their contempories lamented), leading to a lot of persuasive idiots in the assembly.
Memorably, late in the Peloponnesian War, Sparta (who were winning) offered Athens an opportunity to end the war with no reparations. A pretty good offer, you'd have thought, but some people were making good money off the war and they spoke convincingly in the Assembly to persuade the people to keep fighting.
Greek democracy had problems, but I wonder how much of our picture of them derives from source bias. Thucydides, Aristotle, Plato, Xenophon: none a fan of democracy (and Plato to me seems actively dishonest). Writings in its favor would face obviously greater trouble making it to us through Roman and medieval times -- and most of what was written did not make it, on any topic. What do we still have from democrats of the time? I'd like to know.
The above was what I remembered from my Classical Civilisations lessons back in Secondary School (some 25 years ago). I'm very good at remembering stories but not so good at remembering dates, which meant that my prowess in Modern World History and Classical Civilisations was a bit...mixed.
Memorably, late in the Peloponnesian War, Sparta (who were winning) offered Athens an opportunity to end the war with no reparations. A pretty good offer, you'd have thought, but some people were making good money off the war and they spoke convincingly in the Assembly to persuade the people to keep fighting.