Here is the paragraph in question:
"Bring your right hand toward your left hand and peel off the face card (Ace of Diamonds) with your left thumb onto the face of the left-hand packet. Repeat this twice more, singly peeling the Ace of Clubs, then the Ace of Hearts, onto the face of the left-hand packet. (Your right hand is now holding four cardsa face-up Ace of Spades followed by three double-faced cards with the Ace sides up.) Without pausing, bring your hands together as if you are going to peel another card. However, the instant the right-hand packet is over the cards in the left hand, the left first finger flips the lower portion of the packet face down. Place the right hand packet on top and immediately spread the top four cards to display the four Aces."
Nowhere does it say to do a Half Pass (and if I had meant that a Half Pass should be done at that point I would have written "do a half pass"). Besides, no one who does expert sleight of hand would ever use his left first finger in doing a Half Pass--it creates unnecessary and suspicious movement.
(In fact, I doubt that Derek would have used his first finger to flip the packet over here--it's not his MO. He would have pulled down on the inner right corner with his pinky and flipped the packet over that way.)
The text is plain and straightforward. Just do exactly what it says and the sequence works perfectly.
I have to disagree with Christopher, however, in that there IS a discrepancy: if the audience sees three face-up Aces peeled on top of the left-hand packet, and the left hand packet is then openly turned over, and then the right hand places a single Ace face up on top, you should NOT see four face-up Aces when the cards are spread. Forget the fact that the Aces are face up--they shouldn't even be there!
This is the type of discrepancy that worries cardmen and no one else.