(1) Not all errors damage credibility (in my eyes) to a significant degree.

(2) Nonetheless, even if an error doesn't damage your credibility, avoiding it shows that you care about not wasting your readers' time.

To expand on point (1), I'm inclined to be pretty forgiving if

• the error was in a routine computation;

• the computation is almost as easy to do myself as to verify; and

• the computation serves only as an example, not as a formally necessary part of the description of the ideas.

In some fields of mathematics, papers are almost entirely prose, with very little computation (in the sense of manipulating formulas). In these fields, the proofs are communicated using words, not equations, though the words have very precise definitions.