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This is a continuation of the discussion Would a new tag for mistakes/typos/errata for books be useful/appropriate?, where it was suggested that the FAQ might contain guidelines concerning the question:

I have found an error in a book/paper, what do I do?

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  • I have found an error in a book/paper. What do I do?

It might happen that an answer to your question has revealed a mistake in the book or paper you are studying. It is generally good practice to notify the author about such a mistake. Many authors maintain a list of errata (errors), and the error can be corrected if a new edition of the book is published. In this way you can help other people studying the same book. If it is a serious mistake in a paper, the author might even publish an erratum.

Search first: You should always try to find, whether the author or publisher has provided a list of errata online. It is possible that the same mistake was already pointed out and maybe even corrected in a newer edition.

Be polite: It is impossible to completely avoid mistakes in long texts. Authors of books try their best to prepare good books and eliminate mistakes and misprints. Please be respectful towards them.

Use your best judgement: For books, it makes sense to notify the author even if it turns out that the mistake is in fact just a typo. For papers already published in scholarly journals, the author should be probably contacted only if there is a serious flaw in the paper.

For further reference, you may consult also this discussion at MathOverflow.

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Very nicely written guidelines! – Willie Wong♦ Jul 25 '11 at 17:34
I don't understand: "For papers published in scholarly journals, the author should be probably contacted only if there is a serious flaw in the paper." What is the rationale behind that avice? See also the highest-voted answer on MO and the comments there. – t.b. Jul 26 '11 at 2:26
@Theo The rationale is that journals don't prepare 2nd and 3rd editions of their Vol. 146 No. 2 issue. So the only way errors get publicly corrected is through errata in the same journal, sometimes published years later, or through independent articles by the same of by different authors. Neither would happen because of a typo, or even of many typos. Even if the author forgot to state an assumption in the main theorem, which is then obviously used in the proof, he will often not think that an explicit correction is justified. I guess, if the paper is also on the arXiv, that changes things. – Alex B. Jul 26 '11 at 6:31
@Theo: It was meant to be in a similar sentiment as this text taken from the MO question: I am not referring to a spelling typo, that is definitely not important! It's just possible that this typo could confuse someone reading the paper. But I agree that the wording I used is contradictory with the MO thread, which I was unaware of when writing this. (But I still do think that there is a distinction between books and papers - book has a chance of a new edition, even minor typo is worth correcting.) Feel free to change the wording or omit that part completely, if you think it would be better. – Martin Sleziak Jul 26 '11 at 6:45
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@Alex, @Martin: Thanks for the explanations. I agree that there is a distinction, and that for papers typos and minor glitches should be mentioned only if you have something else to say. I guess it also depends on how old the paper is and who the author is. I doubt I would contact a Fields medalist about such a minor thing. On the other hand, if I read a paper by a junior person and caught some issues, I would probably say something (in the form of a by the way: I noticed ...) just in order to let them know that somebody read their work attentively. The formulation is fine as it is.` – t.b. Jul 26 '11 at 10:20
@Theo: precisely. I think such minor typos are also extremely important to point out when the paper is being refereed or in the the pre-print phase, regardless of whether one is dealing with a junior or senior mathematician. – Willie Wong♦ Jul 26 '11 at 11:39

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