TITLE: When is an erratum necessary?
QUESTION [33 upvotes]: A typo, a spelling error etc., in a published article, is definitely not enough for issuing an erratum.
If a mistake destroys a main result, then an erratum is definitely necessary, and the proof should be rewritten, if it's possible to fix.
What about cases in between?  What if a small lemma, remark is not correctly stated?  What about a mistake in the proof that is actually very easy to fix? What about a wrong number in the calculation? What if ... (you name the case) ...?

REPLY [9 votes]: Checking MathSciNet in the five-year period from 2010 to 2014, there were 1319 entries with "erratum" or "errata" in the title.  Sampling a few dozen of them, most cases involve a misstatement severe enough to affect the statement of a theorem.  In a few cases, something was inadvertently left out, such as MATLAB code or an author's name. For perspective, during this period, there were 525795 items added to MathSciNet.