[verylongaccount]

Hear, hear. I would add one thing: make sure that you don't advance claims without evidence (this goes for all scientific enterprises, not just writing reviews). Just because your review is anonymous, do not think it excuses not upholding the basic standard of science: all claims must be stated as clearly as possible and supported by evidence.

[nernst]

Felt this was glossed over. It's all well and good to not be too harsh for the reasons they mentioned, but ultimately the point is to 'peer review' the science.

In fact I would say an important "mistake reviewers make" is ... not actually doing much work. I've seen some appalling 2-3 line comments like "seems fine", even from senior academics. That's not even to talk about problems with misunderstood p-values, not reading the algorithm closely, not walking through the proof manually, and so on.