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.