Instructions
Press "Start" on your controller to go into "Pause" mode. From the pause menu, scroll to "Skip Cinematic" with the arrow keys and then press "X" on the controller. This method will only work with some of the cutscenes.
Back up slightly just before you enter into a conversation with someone. Hold the "High Profile" button, then jump toward the person.
Press the "Lock On" button while you are jumping so that the person begins to speak while you are still in the air. He will start talking and you will land on him and nudge him so he will stop talking, but you will be able to advance to the next portion of the game.