I wouldn't say that he doesn't know what he is talking about, but Vieira is a bit of a gadfly in legal circles-- he routinely publishes pieces arguing that the Federal Reserve is unconstitutional, and other non-mainstream legal theories.
In this case, he's wrong because there is a common-law rule called the "enrolled bill doctrine," which has been followed by the U.S. Supreme Court, that says that if a bill appears in the official journals of the House and Senate, it is conclusively presumed to be a valid law, and the courts will not consider any arguments that it was not properly enacted.
Actually, the FEd Reserve is unconstitutional