While Brutus of Shakespeare's Julius Caesar is initially depicted as noble and idealistically reasonable, he does later display some vanity and unreasonableness. First of all, in Act I, Scene 2, the soliloquy of Brutus reveals his idealistic thinking as he reasons that Caesar will exhibit "abuse of greatness [that]disjoins/Remorse from power...(2.1.18-19) and become corrupt and too ambitious. Later, after the assassination of Caesar, Brutus explains to the plebeians his noble intentions,
Not that I loved Caesar less, but that I loved Rome more. Had you rather Caesar were living, and die all slaves, than that Caesar were dead, to live all free men? (3.2.22-24)
However, Marc Antony deceives Brutus into allowing him to give an oration after Brutus addresses the Romans in Act III, and then incites a riot which effects a civil war. After becoming engaged in this war with the triumvir of Marc Antony, Octavius Caesar, and Marcus Aemilius Lepidus, Brutus argues with Cassius in Act IV, Scene 3 about money and bribes, becoming rather unreasonable, telling Cassius he is "yoked with a lamb/That carries anger as the flint bears fire" (4.3.120-121) although Cassius has shown great reasoning in Act III in advising Brutus not to allow Antony to give an oration.
Further, Brutus exhibits unreasonableness when he insists that he is right about having the troops march to Philippi rather than wait on the triumvir's troops as Cassius suggests, ironically using Cassius's own phrase against him,
There is a tide in the affairs of men
Which, taken at the flood, leads on to fortune;
Omitted, all the voyage of their life
Is bound in shallows and in miseries (4.3.244-247)
Brutus is also vain in that he does not allow himself to grieve for Portia after learning of her death, but instead focuses upon his own concerns. Ironically, Antony lauds Brutus after his death as "the noblest Roman of them all." Perhaps, then, Brutus's later vanities have been temporary and caused by the stress of battle.
Well, to add on and/or clarify, Brutus does display vanity and is seen to be unreasonable. However, in general, he is more guided by his ideology, his loyalty to his country, his principles, and partially due to his bloodline, as Cassius clever points out in his attempt to convince Brutus, that his ancestor, Brutus the Great, would have done anything to rid Rome of a tyrant, in this case, Julius Caesar. Under pressure, however, such traits display, but this cannot account for an overall picture of him in general.
The most substantial evidence to prove that Brutus has an instance of vanity would be that he does grieve over Portia's death.