Julius Caesar creates a grave mood in the audience. Although the play opens with a bit of levity, as Flavius and Murellus walk amongst the commoners and Shakespeare has a bit of fun with wordplay, by the end of the very first scene the tension between Caesar and his political rivals becomes clear.
As the play progresses, Shakespeare makes ample use of dramatic irony to draw a suspenseful mood over his audience that only grows more somber as Caesar draws closer to his assassination and, after his death, as Rome begins to descend into the meaningless violence of war. The severity of the many speeches in Julius Caesar and the lack of any major comic relief enforces the significance of the play's events, and ensures that the audience will take them seriously.
Shakespeare composed Julius Caesar as a sort of warning against the kind of political violence that threatened take root in Elizabethan England at the time of his writing, and by forcing such a serious mood over his audience, he saves Julius Caesar from feeling like mere entertainment. Even where his characters' dialogue descends into melodrama, as with the over-the-top taunts traded between Brutus, Cassius, and Antony in Act 5, Scene 1, the seriousness with which the characters themselves approach their predicament in the play ensures that the audience will do the same.