What are some strengths of Mark Antony in Shakespeare's Julius Caesar?

Mark Antony is persuasive, politically savvy, and ruthless. 

Mark Antony took advantage of Caesar’s death, even if he wasn’t complicit in it. He convinced Brutus he would go along with whatever the conspirators had planned, but then used the pulpit Brutus gave him to sway the people of Rome to his side. Antony also tried to get Octavius to follow his lead, but that was a little more difficult. 

When Caesar was killed, Antony acted immediately. He sent word to Octavius not to come into the city, and then arranged a meeting with Brutus. Over Caesar’s dead body, Antony shook hands with the conspirators and convinced Brutus let him speak to the public. 

Antony uses his speech to turn the people of Rome against the conspirators. He starts off by seemingly praising Brutus and the others, but it soon becomes clear he is actually accusing them. 

O masters, if I were disposed to stir
Your hearts and minds to mutiny and rage,
I should do Brutus wrong, and Cassius wrong,
Who, you all know, are honourable men:
I will not do them wrong; I rather choose
To wrong the dead, to wrong myself and you,
Than I will wrong such honourable men (Act III, Scene 2).

Antony's speech works; the now-angry mob runs the conspirators out of town. Antony joins forces with Octavius and Lepidus, and the three of them begin a transcription. Antony feels he has the most military experience and should be in charge.

Antony demonstrates his ruthlessness with his callous reaction to his nephew’s conscription. 

LEPIDUS

Upon condition Publius shall not live,
Who is your sister's son, Mark Antony.

ANTONY

He shall not live; look, with a spot I damn him.
But, Lepidus, go you to Caesar's house;
Fetch the will hither, and we shall determine
How to cut off some charge in legacies (Act IV, Scene 1).

Antony tries to convince Octavius to agree to do what he says, but if Antony says to go left, Octavius wants to go right. Octavius's age — he is just a teenager — and relative lack of military experience does not convince Octavius to follow Antony’s lead. This will be a problem later, even though Octavius and Antony's side wins and Brutus and Cassius kill themselves.