In principle, a mathematical paper should be complete and correct. New statements should be supported by appropriate proofs. But this is only theory. Because we often cannot enter into the smallest details, we “prove” wrong statements here and then. I plead guilty, having published myself one or two false (fortunately minor) papers.
So far, this is not harmful. The research community is able to point out incorrect statements, at least among those which have some importance in the development of mathematics. In time, the errors are fixed; this is the role of monographs to present a universally accepted state of the art of a topic.