When I apply for a job can my potential employer review my social media listings?

Yes. Today, many employers when considering hiring prospective employees scan the various social media websites to determine if the applicant has a presence on those websites and, if so, what the page says about the applicant. You therefore should clean up your social media pages to remove any images or content that you believe might give an employer concern about you (and keep it clean, if hired) so that your employer will get the correct impression of you as an employee. 

However, as of July 1, 2015, Virginia code section 40.1-28.7:5 prohibits employers from requiring employees to provide social media passwords or requiring employees to include supervisors/employers on social contacts or friends list with access to your social media account.