The plugin does not validate and escape some of its shortcode attributes before outputting them back in the page, which could allow users with a role as low as contributor to perform Stored Cross-Site Scripting attacks which could be used against high privilege users such as admins.
Exploit shortcode:
[ea_full_calendar column_header_format="'}); alert(1); jQuery('#xss').fullCalendar({xssVulnerable:'yes"]