This was a common technique by Shakespeare that he used in many of his plays. In JC, in addition to the commoners speaking prose, Casca (who wishes to sound simple to those around him) speak in prose as does Brutus when address the commoners after the assassination (most likely in an attempt to speak "at their level". It is at this point in the play that Shakespeare is really able to highlight the difference between prose and verse as Antony addresses the crowd in verse which places himself in higher standing than his listeners - an automatic placement of leadership!
Typically, Shakespeare used prose and verse to indicate class or social standing. For example, in Act I, Scene 1, Flavius and Murellus are speaking to a carpenter and a cobbler. Because Flavius and Murellus have been elected as tribunes (representatives) for the working class, they are now of a higher social standing; therefore, Flavius and Murellus speak in verse whereas the commoners speak in prose. Note in Act I, Scene II, the characters are all speaking in prose because they are all of a higher social standing.