Today's historical fiction (Both in cinema and literature) is judged for historical accuracy in so many ways. From chronology to interpretation of events to language and costume. But was this always the case? Specifically regarding Shakespeare's histories.
Did he value historical accuracy in his writing? And how important was this to his audience? Both upper and lower classes.
A few more related questions...
What type of research would Shakespeare, or other playwrights of that era, have done?
Did his plays influence public perception of historical events or personalities?
Most of the events in his "Classical histories" (e.g. Julius Caesar, Antony and Cleopatra) are based on the same histories that we read today- Plutarch, Suetonius, etc. Having studies them both extensively at university, it's fairly clear that Julius Caesar is based mostly off of Plutarch, who, as far as ancient historians go, is pretty reliable.