The Roman crowd in Shakespeare's Julius Caesar does not come off very well. If you take the mob's portrayal in the play as a sign of what Shakespeare thinks of government by the people, I'm afraid Shakespeare must not have thought very much of it.
The crowd is fickle, easily swayed. During Caesar's funeral in Act III, Scene 2, Brutus speaks to them first and by the time he finishes they approve of Caesar's assassination and profess loyalty to and fondness for Brutus. Then Antony speaks, and within minutes they switch their allegiance and are for Antony and against the conspirators.
Then the mob proceeds to riot, proclaiming that they are after the conspirators. But any victim will do for this mob. When they come across a poet who shares the same name with one of the conspirators they kill him, even though they know the poet and the conspirator are two different people. "Tear him for the bad verses!" they yell in Act III, Scene 3.
The mob, then, is not so smart, fickle, and riotous. So much for government by the people.
In Shakespeare's "Julius Caesar," the people are present in two scenes: the one in which Caesar enters the city of Rome, triumphantly; and the one in which Brutus first addresses them, and then Marcus Antony speaks to them. From these three incidents, the reader may conclude that the people follow the crowd syndrome. That is, they are easily influenced by the mood of the moment and the emotions of the majority.
For instance, when Caesar, wearing a laurel leaf around his head, enters Rome, the crowd rides the wave of his glory; they cheer and praise Caesar. Only Marullus seems to recognize the incongruity of the people's behavior:
And do you now strew flowers n his way
That comes in triumph over Pompey's blood?
Run to your houses, fall upon your knees,
'Pray to the gods to intermit the plague
That needs must light on this ingratitude. (I,i,51-56)
It is the "everyone loves a hero" mentality that captures the people of Rome. Cassius remarks about this attitude, as well, when he refers to the crowd's cheering and hailing of Caesar despite his falling down with a seizure in their presence in the second scene of Act II.
However, after the assassination of Caesar, Brutus speaks to the crowd, saying that they "may the better judge" explaining that Caesar had become too power hungry; Caesar was killed because Brutus loved Rome more:
I slew my best lover for the good of Rome, I have the same dagger for myself, when it shall please my country to need my death. (III,ii,45-48)
To this, the crowd shouts, "Live, Brutus! Live, live!
Then, Marc Antony addresses them; and, employing much rhetoric, he is able to sway the crowd into yet another direction, suggesting that Brutus and the others were less than honorable in their intentions. One plebian remarks, "Methinks there is much reason in his sayings (III,ii,109), and others fall in line with his opinion effecting the swaying of the crowd against Brutus and the other conspirators. Again the mob mentality develops and someone shouts, "We'll mutiny (III,iii,229) and the first Plebian says, "We'll burn the house of Brutus (III,ii,233).
Capricious and easily affected by the emotion of the moment, or swayed by their leaders, the people of Rome are uneducated and sheep-like, a crowd to be manipulated, just as so many have been manipulated throughout time.