Show that Brutus is an idealist who commits a series of blunders in his role as a politician as well as a military commander.

I really like where this question is coming from. Brutus, as you've already spotted, gets the military decisions completely 100% wrong, which leads Cassius to realise, just before his suicide, that Brutus has given the word too early and brought about their loss at Philippi. Titinius is the one who tells him

O Cassius, Brutus gave the word too early;
Who, having some advantage on Octavius,
Took it too eagerly: his soldiers fell to spoil,
Whilst we by Antony are all enclosed.

At every other point in the play though where there is a decision to make, Brutus gets it wrong. It's unbelievable really that such a disaster of a man has come to be generally regarded by literary critics as somehow heroic and honourable. No way.

I'll give you two cases in point:

Cassius wants to kill Antony as well as Caesar, fearing that Antony, even after Caesar is dead, may cause trouble for the conspirators. This, of course, is exactly what happens in the second part of the play. Brutus, though, is having none of it:

Our course will seem too bloody, Caius Cassius,
To cut the head off and then hack the limbs,
Like wrath in death and envy afterwards;
For Antony is but a limb of Caesar:
Let us be sacrificers, but not butchers, Caius.

Brutus seems keen to divorce "blood" from the murder of Caesar, which itself is shown up in all its deluded idealism when Brutus and the other conspirators are faced with a huge pool of blood and Caesar's body in the middle of it.

Key point here though is that Brutus overrules Cassius. Antony lives. And causes trouble, just as Cassius says he will.

Case point two is when, after the murder, Cassius is furious that Brutus decides to let Antony speak at Caesar's funeral:

CASSIUS Brutus, a word with you.
You know not what you do: do not consent
That Antony speak in his funeral:
Know you how much the people may be moved
By that which he will utter?

BRUTUS By your pardon;
I will myself into the pulpit first,
And show the reason of our Caesar's death...

Cassius, again, is right. And Brutus is wrong: Brutus' speech only serves as a springboard and a touchstone for Antony's own, made in direct contrast to it.

Brutus may have the right ideals, but pragmatically, the man is an absolute disaster.