Hi Jamie,
It would be a bad idea to try to do that becuase it would involve making a hit to the database to determine the site id during the logging event and that could potentially involve other errors while trying to log the original error and could also be a performance problem for general logging.
What I can do is add a config setting to make it log the full url instead of the relative url and then you would know by the url which site is logging the error (at least for logging events that occur when there is an httpcontext.request involved, not all events log an url)
You'll be able to add this to user.config:
<add key="LogFullUrls" value="true" />
This will be in the repository later today.
Best,
Joe