I've been running Multisites for a few months without any errors. For some reason when I checked my websites today one of my slave sites has begun propagating out to all of my other slave sites.

I'm assuming I'll need to restore all of my database tables and reset this up. That said, how did this happen? I need to make sure it doesn't happen again. Is there a log I can review to see if one of my other administrators somehow did this? Are there any known issues or bugs that may have caused this?

Your question is not clear.

JMS does not do anything in the DB.
So I don't see the relationship with a propagation into all the slave sites.

If your question is why a supposed "slave site" display the master website, this is because the domain name is not present in any list of slave sites defined in JMS Multisites "manage" menu.
So check that you have spelled the domain correctly.
Somethimes, this is because your don't have defined the domain with and without WWW.

When you have provided different site name for each website, you can try to use the ..../administrator URL to check that the site name is correct.