Other mistake: When Anne and Peter are looking at the stars, Anne points to a star and Peter knows what star she's pointing to. It is impossible to point to a star and have someone else know exactly what star you're pointing to. Try it.
Other mistake: Close to when Tony Curtis and the nurse are going back to the pink sub, there is one scene where in the far background there are two objects moving on the water each creating a wake. It looks like someone is water skiing. A DVD will likely show this clearer.