Earlier quoted context omitted.
It is absolutely the reviewers job to check citations. Who else will check and what is the point of peer review then? So you’d just happily pass on shoddy work because it’s not your job? You’re reviewing both the authors work and if there were people to at needed to ensure citations were good, you’re checking their work also. This is very much the problem today with this “not my problem” mindset. If it passes review,…
Agreed, and I'd go further. If nobody is reviewing citations they may as well not exist. Why bother?
2. If the paper turns out to be important, people will bother.
3. There's checking for cursory correctness, and there's forensic torture.