In the play Julius Caesar, how does Shakespeare establish that there are some opposed to Caesar?

Shakespeare demonstrates that Caesar has opposition in Act 1 by allowing his opponents to speak against him.

In Act 1, Scene 1, we learn about the mindset of Caesar’s opponents.  Marullus and Flavius are chastising the common people, the Plebeians, because they want to celebrate Caesar’s victory against another Roman general, Pompey.

O you hard hearts, you cruel men of Rome,
Knew you not Pompey? Many a time and oft
Have you climb'd up to walls and battlements,
To towers and windows, yea, to chimney-tops,
Your infants in your arms, and there have sat
The livelong day, with patient expectation,
To see great Pompey pass the streets of Rome … (Act 1, Scene 2)

Marullus and Flavius do not approve of celebrating the victory in a civil war, where Romans died.  They take down the decorations from Caesar’s statue, a move that gets them punished.  We are told later that they were, “put to silence” (Act 1, Scene 2).  The fact that they faced consequences just bolsters the conspirators case, making it seem as if Caesar does not tolerate opposition.

In Scene 2, we hear about how the senators and other members of the Patrician class feel about Caesar.  While Caesar clearly is wildly popular and has support among the common people, as seen by the cheering crowds at the Feast of Lupercal, he also has major detractors.  Cassius comes to Brutus and feels him out, to see if he also is worried about Caesar too.

Cassius tells Brutus that it is their responsibility to overthrow Caesar, because he is too arrogant.  They fear what he will do if he remains in power and only gets stronger, feeding on the people.  Cassius compares them to slaves if they do not act.

Why, man, he doth bestride the narrow world
Like a Colossus, and we petty men
Walk under his huge legs and peep about
To find ourselves dishonourable graves.
Men at some time are masters of their fates:
The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings. (Act 2, Scene 1)

Brutus assures Cassius that he feels the same way.  Also disgusted by Caesar’s behavior are Cicero and Casca.  Clearly they do not buy into the hype of Caesar.  They are also annoyed when the people cheer Caesar for refusing the crown Mark Antony offered him.  They do this three times, which makes things even worse as far as Brutus, Cassius and Casca are concerned.

Shakespeare establishes all of these little discontents before it is even clear that an assassination will take place (for those who do not know their history, at least).  He introduces the conspirators, starting with Cassius convincing Brutus to join, in this act.  Then later, we will better understand why they pursued the course they did, and why they felt that the people would go along with them after they killed Caesar.