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I'm reviewing a paper after minor revisions, and can partially see another reviewer's comments in the response letter.

The other reviewer asks the authors to do X, but the authors argue that it's not worthwhile doing X. I've done things like X myself, and have found it not worthwhile (for the precise reasons the authors state). Thus, I strongly side with the authors on this matter, and I'm thinking about whether I should inform the editor. I'm not sure if I'm meant to do this...

Question: As a reviewer, is it inappropriate to make unsolicited comments on another reviewer's comments?

A related question is In peer-review, is it common for a reviewer to be shown and asked to comment on other reviewers' reports? However, I have not been asked to comment on the other reviewer's comments.

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It is appropriate. You're acting in good faith after all, the editor is likely to be interested in what you say, and you're not harming anyone.

This is however the kind of thing to put in the confidential comments to editor box. The authors don't need to know of friction between reviewers.

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    Nothing wrong with a debate or disagreement as long as it's polite. If everybody agreed on everything nothing would improve. I don't consider this "friction between reviewers" unless you're disagreeing via ad hominem.
    – Lightness Races in Orbit
    Commented Oct 24, 2018 at 9:28
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    Nothing wrong with a debate with the other reviewer, but do it through the editor - it's not something the author should know about.
    – Allure
    Commented Oct 24, 2018 at 9:37
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    Why not? The whole enterprise is for the author's benefit. I see no reason for them not to be party to all the feedback and opinions therein.
    – Lightness Races in Orbit
    Commented Oct 24, 2018 at 9:41
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    It can cause the author to lose faith in the editor if the paper is rejected, or at least make the editor's job harder. See forbes.com/sites/dailymuse/2017/06/16/… point #3 - the same principle applies. Disagreeing with each other before a customer (author in this case) is not good.
    – Allure
    Commented Oct 24, 2018 at 9:47
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    I think it's dangerous to treat the scientific process like a business interaction with your boss, and social conservatism ("don't offend me!") has no place in a rigorous academic method, but we'll have to agree to disagree.
    – Lightness Races in Orbit
    Commented Oct 24, 2018 at 9:48
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From my point of view, it is a task of the editor to make sure that you as a referee only get those parts of the communication which are meant for you. Since the response of the authors to another referee's comments is now available to you (intended or not), it is quite impossible to not factor it into your own consideration.

Therefore, I would point out to the editor that, strictly speaking, this thread of the comments is not originally yours -- but now that you have got insight to those points, you can just add a remark saying that in your professional opinion, you deem the authors' response convincing.

This makes clear to the editor that there might have been a mistake in providing that part of the communication to you, and the editor can decide for themselves, whether your stated opinion should be taken into account for the ultimate editor's decision, or not.

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    I agree with this course of action, but in my field it's normal for authors to write a single response letter to all referees, and nobody worries about referees seeing one another's comments.
    – David Ketcheson
    Commented Oct 24, 2018 at 7:34
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    @DavidKetcheson indeed. In all my response letters so far, I always included all reviewer comments in one document, without worrying about whether they see it or not. Never had a complaint by the reviewers or editors. I believe everyone sees the benefit in this, after all the purpose of this is to make the paper better. Why not?
    – Gimelist
    Commented Oct 24, 2018 at 8:29

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