I don't have as much information about the game as I wish. I played it back in the 80's so it is at least that old. It was a board game typical size and had squares around the edge of the board that you moved around with real life pictures of people. I believe each person was assigned one of the people and they had a role and you tried to either figure out who the spy was or who everyone was. I loved playing at my Aunt's as a kid but last time I went there and thought about it I couldn't find it. Any help would be appreciated.
This sounds like Top Secret Spies, also known as Heimlich and co.
link to bgg
This game came out in 1984. Players are all allocated a secret character and they move around the edge of the board so it fits your description. Players could move any piece but when a piece landed on the safe all characters scored points depending on position on the board.