what a three mistakes brutus makes concerning the conspiracy, and what are the mistakes?

Brutus makes several mistakes, the first and most basic being that he allows himself to be brought into the conspiracy and misled by Cassius into thinking there are more people in support of their actions than there really are. This Cassius does by throwing in fake letters at Brutus's window, signed with various names, in the days leading up to the assassination.

A second and very large mistake is that Brutus agrees to let Marc Antony speak at Caesar's funeral. Cassius has serious misgivings about this and warns Brutus in Act III, scene i, after Antony makes his request, not to agree

"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?" (Act III, scene i)

However, Brutus does not listen. He is confident that, if he speaks first, there will be no problem, saying:

"By your pardon;

I will myself into the pulpit first,

And show the reason of our Caesar's death:

What Antony shall speak, I will protest

He speaks by leave and by permission,

And that we are contented Caesar shall

Have all true rites and lawful ceremonies.

It shall advantage more than do us wrong." (Act III, scene i)

Clearly, Brutus misjudges the influence Antony will have on the crowd. Along with this bad decision, Brutus makes the decision to leave the scene after he delivers his speech about Caesar at the funeral, allowing Antony to speak to the crowd without interruption or challenge. There, Antony soon inspires them to turn against the conspirators.

In a fourth bad decision, when Cassius and Brutus disagree about how they should approach the battle at Philippi, Brutus insists on having his way Cassius believes it is

"Better that the enemy seek us:/ So shall he waste his means, weary his soldiers,/ Doing himself offence; whilst we, lying still,/ Are full of rest, defense, and nimbleness." (Act IV, scene iii)

However, Brutus believes they should march to Philippi:

"Our legions are brimful, our cause is ripe:

The enemy increaseth every day;

We, at the height, are ready to decline.

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.

On such a full sea are we now afloat;

And we must take the current when it serves,

Or lose our ventures." (Act IV, scene iii)

They decide to march, giving up the advantage of the hills, and in Philippi they are defeated by Antony and Octavius's armies.