That's right, we've finally figured out the problem. It will be a while until we can call it 100% fixed, but if you're still having the now-famous "server class tables" error, simply follow the steps below to get ZM:S working on your computer.
First, navigate to your steamapps/SourceMods/ZombieMod Source folder of your Steam installation. Then, edit a file called gameinfo.txt with your favorite text editor. Remove the following entry and save:
Now restart Steam, launch ZM:S, and you should be good to go! As of now, the side-effects include some missing textures and loss of data, but both of these will be fixed in v1.50, which should be out sometime mid-June.
Thanks for your cooperation everyone and enjoy!