These issues can be fixed by temporarily reverting back to 30 fps. (This is not a fault of Rockstar's, just the game engine) Since Bully was never intended to be played at 60 fps, some issues are known to occur. Otherwise the game may play at double speed if your FPS exceeds your monitors' refresh rate.
I did make a mistake with this video: set your FPS limit to your monitors' refresh rate and enable VSync.