Football is a contact sport, so obviously there will be some "violent" play.
Athletes are often injured, sometimes seriously. Injuries are sometimes shown on-screen but they make a point of cutting away quickly for the sake of young audiences (it didn't used to be that way however, so some older games may show injuries up close and in graphic detail).
Every once in a while, athletes will get into physical fights with each other or referees. Sometimes there will be small riots among the fans, such as throwing beer bottles at referees.