Reproduce: I click “add an event”, then click in the Start Date/Time box or End Date/Time box, the calendar pop up does not work but I can enter the dates manually. However, if I try to set a recurring pattern, the calendar pop up still does not work and I am not able to enter the date in that end date field manually.
I disabled all plugins, then enabled them one by one to determine which one was causing the issue. It appears to be the Tribulant Newsletter Plugin.
Setup: WordPress 3.2.1 | The Events Calendar 2.0.2 | Events Calendar Pro 2.0.2 | Custom Theme | Tribulant Newsletter Plugin 3.8.7
Note: I also tested this with the Twenty Eleven theme and had the same issue