Are spelling issues part of the reviewer's job? During peer-review, is it part of the job of the reviewer to check the spelling, typos, grammar, and suggest improvement? It will help the paper and seems part of the job, but seeing some manuscripts it could take ages to write down every tiny correction in the review.

So, is it the job of the reviewer to judge quality of the writing?
The simple answer is no. Unless the review instructions ask for such comments, it is not mandatory. When I do a review, I usually do some corrections if there are not too many of them. If the paper is littered with such errors I might make corrections for one or two manuscript pages and then state to both authors and editors that the papers needs substantial checking and correction beyond my capacity. I also sometimes just leave that comment without making example corrections.

One of the more problematic issues is the difference between native English speakers and this who have English as a second or third language. Clearly authors who are not native speakers, should receive more help than others. There are also services that do language corrections and each publisher typically can suggest such services. If there are native English speakers as co-authors, some responsibility should fall on them to correct the language, after all, they are credited, or perhaps discredited, by the paper as well. So my point is that some leniency has to be considered depending on the severity of the problem but the bottom line is no-one is forced to correct spelling and grammar.