On the question of period appropriateness, was Shakespeare indifferent, or ignorant? Was Cleopatra dressed in kirtle and wimple because it didn't matter or because he didn't know any better?
Bit of both. The knowledge base Shakespeare and his contemporarenous Elizabethan playwrights had to draw on was a lot narrower than our own, but he never let the stated facts of a story get in the way of whatever he'd prefer to do.
It's also a matter of differences in our cultural conventions. We've inherited this notion of storytelling that tries to accurately reflect reality, to the point where we like our movies and our plays to even look
like completely accurate re-creations of physical reality. The Elizabethans, however, had a completely different set of theatrical conventions; to them, the theatre was a means of communication
, and the presence of the author was not something that had to be hidden away as it is in modern conventions. They weren't concerned with trying to be too realistic, because Realism/Naturalism wasn't a convention that had yet developed. That goes beyond things like using conventions such as the soliloquy or "breaking the fourth wall" (of course, they had no concept of a "fourth wall") by having players speak to the audience -- they were often perfectly happy to depict ancient cultures in modern costume, for instance, and had no qualms about projecting their cultural values into others. Plays had a deliberately artificial quality to them that we're just not generally as familiar with in the modern era, and the idea of trying to make the audience "suspend disbelief" and forget they are seeing a play just wasn't a meaningful concept for them.
Add to this the fact that the theatre was, at the end of the day, a mechanism for propaganda as much as it was anything else; all plays had to be approved by the Master of the Revels, and theatrical performances were subject to heavy censorship from the Elizabethan/Jacobian dictatorships. Elizabethan/early modern authors were very conscious of the fact that they were shaping the public's understanding of historical events for political purposes -- this was not something they shied away from. Hence why King MacBeth is the epitome of temptation and corruption, and the ancestors of King James are depicted so heroically.