With enough exuberance and selective interpretation it is possible to make Shakespeare seem a veritable committee of talents.

From Shakespeare The World as Stage by Bill Bryson.  Chapter 5 page 107.

Much is often made of Shakespeare’s learning—that he knew as much as any lawyer, doctor, statesman, or other accomplished professional of his age. It has even been suggested—seriously, it would appear—that two lines in Hamlet (“Doubt that the stars are fire / Doubt that the sun doth move”) indicate that he deduced the orbital motions of heavenly bodies well before any astronomer did. With enough exuberance and selective interpretation it is possible to make Shakespeare seem a veritable committee of talents. In fact a more sober assessment shows that he was pretty human.

He had some command of French, it would seem, and evidently quite a lot of Italian (or someone who could help him with quite a lot of Italian), for Othello and The Merchant of Venice closely followed Italian works that did not exist in English translation at the time he wrote. His vocabulary showed a more than usual interest in medicine, law, military affairs, and natural history (he mentions 180 plants and employs 200 legal terms, both large numbers), but in other respects Shakespeare’s knowledge was not all that distinguished. He was routinely guilty of anatopisms—that is, getting one’s geography wrong—particularly with regard to Italy, where so many of his plays were set. So in The Taming of the Shrew, he puts a sailmaker in Bergamo, approximately the most landlocked city in the whole of Italy, and in The Tempest and The Two Gentlemen of Verona he has Prospero and Valentine set sail from, respectively, Milan and Verona even though both cities were a good two days’ travel from salt water. If he knew Venice had canals, he gave no hint of it in either of the plays he set there. Whatever his other virtues, Shakespeare was not conspicuously worldly.

Anachronisms likewise abound in his plays. He has ancient Egyptians playing billiards and introduces the clock to Caesar’s Rome 1,400 years before the first mechanical tick was heard there. Whether by design or from ignorance, he could be breathtakingly casual with facts when it suited his purposes to be so. In Henry VI, Part 1, for example, he dispatches Lord Talbot twenty-two years early, conveniently allowing him to predecease Joan of Arc. In Coriolanus he has Lartius refer to Cato three hundred years before Cato was born.