It is a bit of trial and error, but you could look at the upgrade scripts and see which tables have been added at each level of upgrade, working backwards until the scripts would not make any changes to the DB.
Also, we made a change to some of our sites that were hosted on a server that was upgraded to PHP 4.4 unexpectedly, and got them to run again by suppressing the errors. I will try to find out what changes we made and post them.