What is the issue in act 1, scene 1?

In the first scene of the play, two Roman tribunes named Flavius and Marullus are disgusted that the public is going out of its way to celebrate Julius Caesar's return to Rome. They are loyal to Pompey and fear that the people will try to make Caesar their king. They take down the ceremonial flowers placed upon statues in the city and order people to get off the street and back to work.
This scene sets up the central conflict of the play: the tension between those who support Caesar and his endeavors and those who fear that his popularity will end the Roman Republic. His dissenters believe that Caesar will transform the republic into a dictatorship where one man is put ahead of all others. We see this conflict in miniature here with minor characters.

The issue in act 1, scene 1 involves Flavius and Marullus's disgust that the Roman citizens are celebrating Julius Caesar's military triumph and their fear that the public support will encourage Caesar to become Rome's emperor. Both Flavius and Marullus are opposed to Julius Caesar and feel that he is a threat to the Roman Republic. As the citizens take off work and gather in the street to celebrate and support Julius Caesar, Flavius and Marullus are astonished at the citizens' hypocrisy. Marullus comments on the fact that the citizens have just finished supporting Pompey, and he is surprised that they would celebrate Pompey's opponent, Julius Caesar. At the end of act 1, scene 1, Flavius and Marullus begin forcing commoners off of the street and taking down decorations that adorn statues for the celebration. Flavius's comment at the end of the scene is significant and introduces the conflict in the Roman Senate. Flavius says,

These growing feathers plucked from Caesar’s wing Will make him fly an ordinary pitch, Who else would soar above the view of men And keep us all in servile fearfulness (Shakespeare, 1.1.72–75).