I drew a system diagram on the board and described my process and decisions for creating the application. As I worked on it the interviewers asked follow up questions involving how I would test the system, how I would deal with changes made by Twitter regarding API access, etc.
I iterated over the string and pushed onto a stack each time an open parenthesis was encountered. Each time a close parenthesis was encountered I popped from the stack. If I reached a close parenthesis but the stack was empty I knew there was an unmatched close. Similarly if the stack still had items in it when reaching the end of the string there was an unmatched open.