You state (without reference, so I assume this is not Leibniz'):

Given that God is a perfect being, he could not create anything less than perfectly. Hence this world must be perfect.

But I picked up a Leibniz biography (which I didn't read, yet), and a quick glance suggests that "the best of all possible worlds" for Leibniz means

the world which contains the maximum compossible perfection and goodness

(Antognazza, p. 486).

So, Leibniz didn't think the world perfect, but merely most-perfect, or: best.

You state (without reference, so I assume this is not Leibniz'):

Given that God is a perfect being, he could not create anything less than perfectly. Hence this world must be perfect.

But I picked up a Leibniz biography (which I didn't read, yet), and a quick glance suggests that "the best of all possible worlds" for Leibniz means

[...] the world which contains the maximum compossible perfection and goodness. In short, all the evils of this actual world are logically necessary for the greater good of the best of all possible worlds.

(See Antognazza, p. 486.)

So, Leibniz didn't think the world perfect (as in: free of evils), but merely most-perfect, or: best.