Here is a site which if you for search Julius Caesar will bring up some primary sources for you to compare with Shakespeare. I think he based it on Plutarch wrtings of the man so depending on how accurate Plutarch was...also Shakespeare changed some dates (date of Brutes etc fleeing from city..etc) http://www.perseus.tufts.edu/
Just a small note doesn't he say at one point there is a striking of the clock? eeek no clocks?
So to recap I would read some Plutarch on the subject and see where Shakespeare deviates. Also the works of JC himself and Suetonious etc can be found @ the above link, they would be useful starting points.
Good luck on your studies