Is there (or should there be) a website to record errors in papers
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...