Jack – I love the BMLT Tabbed UI. Loads quicker after the update. I'm copying you on this support request to Time.ly.
Their All in One Event Calendar is a favorite and I have been using the pro version for over a year. My installation is ai1ec 1.11.4-pro on WP 3.8 with twentytwelve theme.
To verify the problem I deactivated ai1ec and determined that trouble was gone. What is happening is that the select2 arrow acquires some padding to the right and obscures the field. I am aware that I need to do some styling to make the content darker.
You can go to the link to see the problem http://fsrna.org/free-state-search
I have been able to determine that it is related to select2, but further investigation is beyond my capabilities. I really do want both of these plugins to work. I have passed this request for support on to the designer of the BMLT Tabbed UI. If there is a way to remove the select2 option from AI1EC I would not complain. I tried it and didn't like what it did with the calendar view, with Display single- select and Categories multi-select.
A link to the calendar is here http://fsrna.org/calendar and included with the topic. - Louis