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The philosopher Rebecca Newberger Goldstein writes in her book Plato at the Googleplex: Why Philosophy Won't Go Away (published in 2014):

Plato got it about as much wrong as we would expect from a philosopher who lived 2,400 years ago. Were this not the case, then philosophy, advancing our knowledge not at all, would be useless. I don't think it's useless, so I'm quite happy to acknowledge how mistaken or confused Plato can often strike us.
What Plato did was to carve out the field of philosophy itself. It was Plato who first framed the majority of fundamental philosophical questions. He grasped the essence of a peculiar kind of question, the philosophical question, some specimens of which were already afloat in the Athens of his day, and he extended their application.

Gary Gutting, who teaches philosophy at Notre Dame, warns that we should consider Plato in the context of his time and place.

My take on Plato (with more help from others) begins here.

Plato (c. 424–348) was among those associated with Socrates who fled Athens following Socrates' execution in 399. Like Socrates, he was dissatisfied with the world, but rather than see remedy only in individuals improving themselves, as Socrates seemingly did, Plato saw remedy in new institutions. As Karl Popper wrote in The Open Society and Its Enemies, Plato was big on social engineering.

Plato became the most influential of the ancient writers and was adopted by the Roman Catholic church. In his book A Little History of Philosophy, published by Yale University Press, Nigel Warburton wrote, "Plato believed that only philosophers understand what the world is truly like." Truly like? The common man who hurt his toe on a stone, according to Plato, had no idea about the hardness of stones. Plato believed that only those who thought like he did who knew the essence of reality.

Plato wrote an allegory that has impressed a lot of people. His cave allegory is well known. Wikipedia describes it as follows:

Plato has Socrates describe a gathering of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe names to these shadows. According to Plato's Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

A philosopher, wrote Plato, is a man who loves the "vision of truth." For Plato there wasn't truth in sense experience. Plato saw truth in idea that is essentially spirit and essentially permanent. He saw truth in abstraction. His claim was, as Warburton writes, that if you wanted to understand goodness "then you need to concentrate on the Form of goodness, not on particular examples." It made him anti-particular, anti-specific and an enemy of science.

Change for Plato was in the world of perceptions, the world of shadows. Plato rejected the views of Heraclitus that reality was a process, and he rejected Heraclitus's belief in evolution. Plato rejected the atomism of Democritus and Democritus's idea of development and decay. Like Pythagoras (c. 570–495), Plato believed in perfection and saw perfection in mathematics. And like Pythagoras he saw mathematics as more than established rules regarding relationships between numbers, and more than imaginary abstractions. He gave to numbers the same kind of essence that he gave to words: a god-given essence. Words for Plato had unchanging essences, something beyond social conventions that change in time.

Plato looked to the heavens and assumed that there were perfection and permanence just as in mathematics. He believed that the heavens consisted of perfect spheres and circles. Like Pythagoras, he made harmony fundamental to his philosophy. Here we have the perfect order that some today believe that Almighty God created. The world that Plato believed in consisted of perfection and justice and the eternal soul. He rejected the idea of conflict in nature. He assumed that a person's soul has its rational side and its irrational side, that on one side was mind and the ability to reason and on the other side was desire – what some would call impulse. Plato assumed that a person served his or her soul by denying oneself the bodily desires of the material world. He believed that the part of the soul that was mind (consciousness) survived death while desire did not – ideas that attracted Christians in the early Middle Ages. Melding philosophy and religion, Plato believed that the highest activity of an individual was to contemplate the beauty of God and the immortality of his own soul.

Plato wanted to take politics out of the world of the senses and create a perfect political arrangement in the form of a utopia. He wrote a book, Utopia. He formulated a society run by a group he imagined were sound philosophers like himself, certainly not someone like Thomas Jefferson, whom he would have despised. Democract according to Plato led to degeneration. Plato's philosopher-rulers had to be authoritarian. He decided that it should be official doctrine that class divisions had been created by Zeus (God), and he thought that citizens of his republic should be obliged to believe in God. Plato decided that the reading of certain kinds of literature should be forbidden, among them the works of Homer or stories that depicted virtuous people as unhappy or villains as happy. Plato, in other words, had devised a totalitarian order.

His utopia was impractical. No one who had any political power or influence, including kings or oligarchs, were willing to surrender their power – despite claims by otthers of possessing Truth. No band of Platonic philosophers would find an army of men willing to fight to overthrow an established power. Politics continued to be a struggle among established cliques with common economic interests. Plato's utopia would never came to be

And in time "the heavens" were discovered to consist of other than perfect circles and perfect order. Plato's attempt at knowledge through what he thought was critical thinking was supplanted by the methodology of science – eventually accepted as valid by the Catholic Church.

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