What is Shakespeare's purpose in having Mark Antony describe Lepidus in such derogatory terms?

To defeat Brutus and his coconspirators, an alliance of three men, or triumvirate, is established. The members of this triumvirate are Octavius, Mark Antony, and Lepidus. It's little more than a marriage of convenience, as the three men have radically different temperaments, each one seeing himself as Rome's sole rightful ruler. Mark Antony bears a particular animus towards Lepidus. He regards him as unfit to rule. The glittering prize of political power in Rome would be wasted on him; it'll be like weighing down an ass with gold:

He shall but bear them as the ass bears gold, To groan and sweat under the business (Act IV Scene i).

As Lepidus isn't up to the job, thinks Antony, he should be put out to pasture:

And having brought our treasure where we will, Then take we down his load and turn him off, Like to the empty ass, to shake his ears And graze in commons. (Act IV Scene i).

But Octavius rebukes Antony, reminding him that Lepidus is a brave and valiant soldier. Octavius can see the bigger picture, as it were; he understands that the forces ranged against the conspirators are going to need all the help they can get if they're to prevail. Mark Antony, however, shows himself to be a snob in rejecting Lepidus, someone from a relatively humble background.
In presenting Antony's snobbery and Octavius's instant rebuke, Shakespeare is foreshadowing later events; the triumvirate will collapse, and Octavius and Antony will go to war with each other. Unlike Antony, Octavius doesn't allow social snobbery to get in the way of his military objectives, and he will be rewarded for his practical common sense by a victory that will lead to his becoming Rome's emperor.