The title pretty much says it all. I’ll just add that I’m mostly curious if Cassius was a real person, because I maintained, to the chagrin of my English teacher, that Cassius was the tragic hero of the play. I thought of the four plays by the Bard I’ve read so far, that he was the best character.
I’m no Shakespearean scholar, but I know that Shakespeare’s “histories” tend to play fast and loose with historical fact. Think “Oliver Stone”. 
For its time Julius Caesar was exceedingly accurate as a historical play. Shakespeare depended a great deal on Plutarch’s Lives and I am told a hand full of other references.
The Bard was quite comfortable with both Latin and Greek and did pretty good research. As a matter of fact during the heigth of the “Did Shakespeare write Shakespeare’s plays?” debate one of the arguments against Shakespeare’s authorship was that Julius Caesar was too well researched to come from a glovemaker’s son’s pen.
Shakespeare did take some license with the language and phrasing to be sure. Writing in iambic pentameter will do that sometimes. But generally the whos and whats are pretty accurate even down to Marullus and Flavius at the very beginning of the play. Did they actually go head to head with the Cobbler? Probably not, but they did get put into house arrest for tearing down decorations on Caesar’s statues during the celebration of Caesar’s defeat of Pompey.
Did Artimadorus try to warn Caesar. It is agreed he did. Was there an earthquake and storm on March 14? Experts say yes. Did Marcus Brutus and Caius Cassius die not by enemy swords at the battle of Phillipi but instead by friendly swords? It is also generally agreed to be true.
Did Anthony stand over Brutus’ body and say, “This was the noblest Roman of them all.” Probably not. Did Antony say “Friends Romans Countrymen lend me your ears. I come here to bury Caesar not to praise him…” More than likely not exactly.
Probably it is good to think of the play as a 17th century docudrama. The outline is accurate but some of the specific details might be open to conjecture.
Update: I just got an email from a scholar who suggested that Julius Caesar might be more accurate than more contempory plays to Shakespeare. In those plays Shakespeare had to be more “politically correct” and not insult the relatives of existing monarchs and play down the contributions of rivals.
Like the clock in act 2…I don’t think sundials or hourglasses strike the hour.