Well not really, right? Let's suppose some well known, well respected author that has a history of correct results puts up a new paper. I (and I think most people) will assume that the result is correct. We start to apply more doubt once the claimed result is a solution to a longstanding open problem, or importantly, if the researcher has a spotty track record for correctness (in math/TCS) or falsifying results (in experimental fields).
But really we shouldn't be talking about math errors and falsification in the same category.
But really we shouldn't be talking about math errors and falsification in the same category.