Thanks for this information!
I am still not able to recreate the issues here, and so I’m wondering if perhaps a copy of these plugins is corrupted or something which is causing that error.
To test for this, do you notice any improvement if you DELETE the existing versions of The Events Calendar and Events Calendar Pro off of your site? (This will not delete any event information).
Once deleted, download a fresh copy of The Events Calendar from here → http://wordpress.org/plugins/the-events-calendar
Then download a fresh copy of Events Calendar Pro from here → http://theeventscalendar.com/my-account/downloads
Install those freshly on the site and see if anything improves here; let me know if this helps!
– George