When Eddie gets into the plane to fly to Mexico and pick up Francesca, he starts the plane from the interior. The Piper seen in the film was a model that did not have an interior starting mechanism - someone had to spin the propeller to start the aircraft.
It's true that this particular airplane model did not come from the factory with an engine starter, and needed the propeller to be turned to start it. Many of these airplanes, however, have been modified with starters, and can be started by the pilot, without someone turning the propeller from the outside. This writer has flown one.
The copyright listing at 1:46:27 in the film's end credits is "Copyright © MMIIII by Spin Productions, LLC" which corresponds in Arabic digits to 2004, that contradicts the US Copyright Office records showing Creation Date: 2003; and Registration Date: 2003-10-10.
The filmography feature on the DVD extras lists Stanley Tucci as having played a role in the film "Maid in Manhattan". However, Manhattan is misspelled as "Manhatten".