The scene where Belle (Shelly Winters) dives into the water was actually rehearsed by having her jump into the water. She decided to dive in while filming the scene and that take was used.
The look of the set for the upside down engine room was so real, the actors refused to climb anything, fearing that it would fall. The set designer and builders had to climb it first to prove it would hold.
Just before midnight when the band is playing "Morning After" the camera pans out for a wide shot of the dance floor - the dancers are dancing MUCH too fast for such a slow song - and you do still hear the song.