This plugin will allow you to manually verify your BuddyPress members from the profile edit screen. Verified members will have a twitter-like “verified” badge displayed on the front-end.
A dedicated settings tab allows you to choose where you want to display the badges: in the activities, profiles and/or member lists (e.g.: member directory).
BuddyPress members directory showing some verified users
BuddyPress profile page showing a verified user and user activities
BuddyPress extended profile showing the “Mark this member as verified” checkbox
Plugin settings page