Does Apple maintain a public list of known serious bugs?
Apple does not have a list of publicly known issues/defects/etc. About the only option is to open a bug report with Apple through their Bug Tracking Tool. If the issue already exists in some manner, your opened issue will be closed and marked as duplicate, with the issue number for which yours is a duplicate. 

Sadly and unfortunately, you will not be able to access the information of the "original" issue for which yours counts as a duplicate. Also, it has been said but has not been confirmed officially, that your reported issue will raise the internal priority of said "original."

Note that, this only helps if you know about the issue, to begin with, and report it. If you want to find out about any known/reported issues, the best option available at this time is to use OpenRadar. This site is publicly managed and populated voluntarily, by people who have opened issues with the bug reporting tool mentioned above, and added their information (issue tracking number, details, specifics, status, etc.) to the OpenRadar database.