The problem is noot with WP Super Cache. W3 Total Cache also give same problem. I have tried several other Cache plugins. After a few hours Sidebar login starts “undefined” funky error. So, this is not WP Super Cacche problem, but a bug in Sidebar login for sure.
Developers should have fixed it. I had noticed these type of reports as old as 2 years.
With WP Super Cache plugin the “undefined” error strats immediately once cache is built. With W3 Total Cacche, it take several hours to a couple of dayss for the error to starts appearing.
The only work around I had found which works; is use W3 Total Cache with Objecct Cache and DB Cache disabled. Then, setup a cron job and delete your caches index.html file every couple hour, or for busy sites every 15 minutes.
I am using it with a datingsolution.biz DSP plugin at https://www.shaadiconnections.com. I discussed the issue with the developers of datingsolutions.biz. They will fix the Sidebar login bug for their customers. However, it may be a couple of months when new version of DSP will be released. They will package the fixed version of Siderbar login with their plugin for their customers.