I am so glad I had common sense media to consult for this. At the suggestion of common sense media _did_ preview, and will not be showing this as family fare. After previewing this, I've come to the conclusion that this was never intended to be for kids. Others pointed out a couple of scenes that parents could fast forward through. Even with a quick finger on the remote, I'm left concerned that the emotional impact is inappropriate for my teenage sons.
There are two story arcs here. One is this pure-minded soul, plods along in life and through his gifts -- running, ping pong, etc. -- bumbles into great success, and encounters seminal historical events. That story arc, underpinned by Forrest recalling and following his mother's advice, would be great to share with the family. The other arc is his longing for Jenny, the girl he befriended on the school bus the first day of school. Jenny, either because she's dealing with her own demons or because she feels she'd be taking advantage of Forrest, stays connected with Forrest but won't commit to him until the very end of the movie. In what may be the most poignant part of the movie, Forrest simply asks her "Will you marry me?" and tells her "I would make a good husband." He then says that he is not smart but that "I know what love is." Though masterfully acted by Tom Hanks, it is because of this intense emotional component that I am choosing not to share it with my kids.
I saw someone mention that there was a shorter version, edited for tv. If anyone knows where to find this, I'd be interested. The message for me of the movie is to live one's life with honor. It's a great message; just a little too heart wrenching for me to want to share it with my teens.