Is there (or should there be) a website to record errors in papers There are several questions on this site about errors in papers and even the errors-erratum tag. I'm specifically thinking of mathematical errors, where there is an unambiguous mistake, like a wrong sign or wrong physical constant. I have come across ~5 of these in the past month.

Is contacting the publisher really the best way to correct these? Sometimes papers are old and it seems unlikely that a new PDF will be generated. Would the academic research community find it useful to have one canonical site that made it very easy to submit errors and corrections. Then, when reading a paper, one could check the site with the DOI or title and see if that paper has an entry. I am considering making such a site, but wanted to check with other academics if it seems like a worthy endeavor, if a site like this already exists, or if there is a reason it does not exist.

I realize this is an opinion question. I know these types of questions get closed, but this is still the best site I can think of to ask the question, so hopefully I get some good replies before this gets downvoted.
A site which has some ambitions and potential in this direction is PubPeer, which aims to be a general "online journal club", but which has also become a place to dissect papers for errors and possible fraud, particularly in biomedical areas.  It is thus one clearing house for discussing errors in papers.

Interestingly, they also have apparently set up a system that allows you to use a browser plugin to easily dual-post your comments on PubPeer to comments on the paper at the corresponding journal's site, which may also help with putting pressure on editors to actually make corrections...