Is this correct? “быть устают” seems wrong to me. устают is 3rd person plural. Shouldn’t we have устали or усталными or something like that?
Teachers must get tired of correcting the same mistakes over and over again in their students’ papers.
“Должно быть” is a phrase in itself. Marking it off with commas or moving it to the front of the sentence would help make this clearer to an English speaker. The word “устают” agrees with “учителя”. The meaning of the sentence is something like “It must be the case that teachers tire of encountering the same mistakes from their students.” We would more naturally say “Teachers must get tired of…” but this is at least theoretically ambiguous, since “must” can express obligation as well as likelihood.