It's odd that I've deleted all the files that I uploaded and uninstalled the product and I am still gettting error messages that state the forum.post_thanks table doesn't exist.

I would almost guarantee that the issue is with my lousy host.

If you have a big board it's probably because the installation sequence is still running where it attempts to index each post and check for thanks while building the thanks table and as the table for that now doesn't exist because you've uninstalled it you are now getting the errors.

IS there a way to stop that installation sequence?

You'd have to find the process on your server and kill it either through the server control panel like plesk or using ssh....etc or just wait until it bottoms out.

There may be remnants of the installleft behind which is causing the action, i suggest, close your board, upload the files, reinstall the product, wait for the processes to finish then uninstall.

How do I know when the process is finished? Are we talking about the process of indexing or the process of the uninstall?

processes of indexing. If you install it again it may even correct the issue, but remember with a big board it can take some time and even time out, if it does just start the install again and it should happen quite quickly.

You'd have to check your server for the processes to see whats running.

My board in miniature at best. I'm sure this started due to an issue at my host. It usually times out when I try to upload or install something.

in that case the have the timeouts set too low, or the max_packet set too low

This is caused by using PHP Version >= 5.3.x - Silencing the error inside the post_thanks.php should not be the final solution, since the problem is still there, you only dont see it anymore.
It says the plugin is not supported anymore - any chance somebody else could upgrade the script so that we can use it with newer PHP Versions?

That code is in my post_thanks.php file but I'm still getting the above errors. :(