In real life, Michael Llewelyn Davies was J.M. Barrie's inspiration for Peter Pan. Michael, not Peter, was said to be Barrie's favorite of the children. It's not clear why Barrie chose to name the main character Peter. One idea is that his brothers and Peter behaved the most like an adult at a young age. Barrie wished he'd had more of a childhood, so he immortalized him as the symbol of youth.
During the opening scene, most of the extras wanted to go through the left door so they could shake Dustin Hoffman's hand.
At the movie's end, when J.M. Barrie shows Sylvia the play at her house, Peter Pan asks them to clap their hands to save Tinker Bell. Julie Christie's reaction to this was to start clapping immediately. This was unplanned, and the children had no idea how to respond. The look of shock on their faces is real.
Johnny Depp was so impressed with the performance of Freddie Highmore during filming that when Depp was cast for Charlie and the Chocolate Factory (2005), he specifically requested Highmore to play the title character of Charlie.
During the formal dinner scene, Johnny Depp placed a "fart machine" under Julie Christie's chair. He had a remote control that he used to trigger a fart sound from the device. The children are laughing more at that than from playing with the spoons.