Looking at the replay from NFL rewind (better quality), this is what I see:
1. The lines (red showing the line of scrimmage and yellow showing first down) are exactly where the sticks are.
2. The original spot of the ball (and the new red line when the Pats are originally lining up) is pretty much exactly where Welker landed, which was half a yard shy.
3. The Ref definitely picks up the ball, wipes it off, and puts it down half a yard further down the field.
4. At the same time he is doing this, the chain gang are moving the sticks. They didn't wait for him to move it first, then move the sticks. He must have called first down, then adjusted the ball to make it official. Also, the same ref that originally makes the correct spot moves the ball to the new spot, so there wasn't a different call that over ruled the original spot.
5. The two side refs are lined up on the ball (original spot), and as they're backing up to the sidelines, move over a yard to line up at the new spot.
What all that means...no idea.