What is the meaning of the term “conflicting perspectives," and how is notion conveyed through actions and relationships between characters?

The term in the case of Julius Caesar refers to characters' possessing contradictory or contrasting views of Caesar, Rome, and what should be done.  Literary works such as plays often rely on "conflicting perspectives" because the audience gets to hear the thoughts of a variety of characters (rather than works that rely on first person point of view only or third person limited point of view).

In Caesar, most of the conflicting perspectives stem from how the main characters view Caesar. For example, the people of Rome and many of the senators see him as a noble leader and an undefeatable military strategist who has won accolades and wealth for the republic. Cassius and Casca's view are just the opposite; they see Caesar as a bloody usurper who took his position by force (from Pompey) and who is physically and mentally weak (see Act 1 in which Casca and Cassius discuss Caesar's health problems and his having to be helped across the river).

Similarly, when Caesar refuses the crown three times, the crowd thinks that he is being humble and cry out even more strongly for him to accept it. The conspirators see Caesar's refusal of the crown as a ploy on his part to eventually become king of what is supposed to be a republic.

Shakespeare also gives his audience a perspective of Brutus that might conflict with others' view of him.  At the play's end, Shakespeare characterizes Brutus as "the noblest Roman of all" and portrays him throughout the play as a man who simply wants what is best for Rome. In contrast, in other literary works and in some historical accounts, Brutus serves as one of the best-known backstabbers or betrayers in history (Dante's Inferno couples him with Judas Iscariot), and most historical accounts point out Caesar's last words about Brutus's participation in his murder.

So, when a reader gets several views of a literary character or event in the same work, he/she experiences a conflicting perspective and must determine how the author intends for the character/event to be received.