Erratum or corrigendum on arXiv too? Should the authors lists match?
#1 is best: use arXiv's "replace" option to upload a new v2 with the same arXiv: id, which has the corrections incorporated into the paper.  The arXiv preprint has its own life, independent from that of the published paper, and this makes the preprint as useful and convenient as possible - people following the arXiv id or URL for the original preprint will get the corrected version automatically.

In the comments field, I would put something like "incorporates published corrigendum".  If the corrigendum has its own DOI, I would include it in the comment as well.  (And while you're at it, make sure you've included the DOI of the paper itself in the appropriate arXiv field.)

Keep the authors field unchanged.  People don't really need to know which authors actually wrote the mistake or the correction, so long as all of them accept responsibility and approve the correction.  (Unless there are special circumstances - e.g. the correction is itself a major scientific advance, or the "mistake" was something like data fraud and the guilty party needs to be outed, in which cases you could consider adding a note within the paper itself.)

Note that the original v1 will continue to be available for those who click it explicitly, so anyone who really wants to see the history or compare the versions can do so.