What does Alexander Pope mock in his poem An Essay on Man, and what techniques does he use?

An Essay on Man, unlike many of the other works for which Pope is best known, is not a satire. Mockery is thus not a prime feature of the poem, as it is in The Rape of the Lock or The Dunciad, for example. The ideas in the Essay, however, are put forward partly by showing the falseness of opposing kinds of thought, which Pope does hold up to ridicule, but not with the kind of sardonic or acerbic expression we find in the satires. It's more in a sad or regretful way that Pope demonstrates, or attempts to do so, that those who disagree with his views are misguided.
Though the "best of all possible worlds" philosophy of Gottfried Wilhem Leibniz was later much ridiculed (sometimes in a caricatured version) by Voltaire, for example, in Candide, this forms the basis of much of Pope's thinking. Pope's view is that it is wrong to regard the negative aspects of the world, the imperfections of life, as evidence that God is unjust—or worse, that God does not exist. To Pope, it is a sign of naivete or foolish pride for anyone to expect the world to be perfect, without problems and challenges for man to solve. It's also a sign of narcissism for man to think the universe was created for his personal benefit or comfort, because we have no way of knowing exactly what God's larger plan or overall purpose was in creating it. It's the self-centered, prideful view that Pope holds up to ridicule, through striking metaphors and, as with all great poets, his brilliant and beautiful word choice.

Ask for what end the heavenly bodies shine,
Earth for whose use? Pride answers, "'Tis for mine:
For me kind nature wakes her genial power,
Suckles each herb, and spreads out every flower . . .
Seas roll to waft me, suns to light me rise,
My footstool earth, my canopy the skies."

Pope's language is so striking that even those who don't agree with his views find it difficult to avoid quoting him once they have read his work. This is why Samuel Johnson (who disliked the Essay on Man despite his view that "if Pope be not a poet, where is poetry to be found?") referred to the "blaze of embellishments" with which Pope had expressed a philosophy Johnson himself considered absurd. Pope does not so much mock as express in sublimely powerful verse his view of those who disagree with him as unfortunately misguided and unrealistically prideful. As noted, there is a sad, regretful tone that dominates much of the poem in contrast to the slashing, merciless style of Pope's satiric works.