Forrest Gump is a great commentary on American life from the 1950s-1980s. You can easily take a tour of history through the people that Forrest encounters (Elvis, JFK, LBJ, Black Panthers, etc.) and events (Vietnam, Attempted Ford assassination, invention of Apple Computers, etc.). I question whether or not even a 13 year-old will fully get this movie as they may or may not know about some of the events that take place. Having said that, because Forrest is such an affable character and has such a true love for Jenny, even an 11 year-old will find this movie fun to watch.
If there are any disturbing scenes in this movie, you can easily imagine as to what they are--the suggested abuse Jenny gets from her father (even thought it doesn't show anything), Forrest's encounter with the Black Panthers and former Alabama Governor Wallace (the N---word IS used), and the violent war scenes from Vietnam.
Forrest is a great friend and has the most pure and innocent love one can imagine. Good values children can take away are things like: the value of friendships, the value of true love, respecting one's parents and elders, serving our country, nobody likes to be teased, and to treat others like you would want to be treated.