Learn Italian: Malgrado il guasto, avevamo continuato il montaggio. - Despite the breakdown, we had continued the setup.

Yes, malgrado and nonostante are completely interchangeable when followed by a noun. Both mean "despite" or "in spite of", so you could perfectly well say Nonostante il guasto.

Why does continuare use avere (avevamo continuato) as its auxiliary here? Doesn't it sometimes take essere?

Good memory! Continuare takes avere when it acts as a transitive verb with a direct object, which in this case is il montaggio. It only takes essere when used intransitively, for example if the subject itself is the thing continuing (like La pioggia era continuata, meaning "The rain had continued").

Is guasto only used for mechanical breakdowns?

It is mainly used for mechanical, electrical, or technical failures, such as a broken machine, a stalled car, or a server outage. It comes from the verb guastare (to break or spoil), which can also be used for spoiled food or ruined plans.

I've seen montaggio used to mean film editing. Does it also mean "setup"?

Yes! The core meaning of montaggio (from the verb montare) is "assembly" or "putting things together". While it translates to "editing" in a film or video context, here it refers to the physical assembly or setup of equipment, furniture, or a stage.