This is a great film, if you use your common sense!
I found it very funny that so many parents were scandalized by the story. It is a modern retelling of classic literature: Dickens' Oliver Twist! A good gauge to tell if your child is ready for it is whether or not you would consider screening OLIVER! (another G rated musical based on the same story) for them.
Otherwise, this is a terrific little film. The characters are engaging, and now, 30 years on, it captures the look and feel of 1980's New York City brilliantly. The opening sequence, depicting Oliver's struggle to find shelter to the lovely tune of "Once Upon a Time in New York City" never fail to bring me to tears.
I appreciate that Jenny, the little girl who adopts Oliver, is portrayed as a real little girl, kind and loving, but also a tiny bit willful as well. The characters, aside from Oliver, Jenny, and possibly Jenny's faithful butler Winston, are not the best role models, but in the real world, none of us are perfect. However, like Fagin and his gang, we can all be our best selves when we need to be.