Look at the source of this error "InnerException:Unhandled Error Adding Module to LeftSideFullA". I am not sure if the whole module is not being loaded. If the whole module is missing in the page, you should notice it's missing. If you are able to identify which module it is and it's not needed, uninstall it. As long long as you don't find the root cause of the problem, this error will happen, it will get logged and the database will get larger. Truncating the event log table only, whether frequently or not, is just removing the symptom. Find out which module it is.

I think "LeftSideFullA" is the name of the pane in the skin where the module is being injected to. Try switching to another skin and see if the error goes away. Maybe it's a skin issue.