It's a debate I started in the shoutbox. So, if you go onto the roof and look down, you'll that that is a pool of blood along with a blood smear where Reggie's body once was. I personally think he turned, as his brain wasn't fully destroyed on impact, and dragged himself away.
(Shoutbox stuff ahead) There was a walker in 400 days that had a screwdriver in their eye. It wasn't deep enough to put the walker down but it probably did penetrate the brain. If Reggie only had his brain partially damaged, then he could still turn. You see, the cop (400 days walker with screwdriver) was struggling to move, due to the screwdriver in it's eyes, meaning the tool damaged its brain in some way that it had trouble moving, but not damaged enough to kill it. Same with walker Reggie. This is because there's a part of the brain, at the back, which controls movement. Penetrate that part of the brain, and you kill the zombie. If pieces of Reggie's skull didn't dig into this important sector of the brain, then he could indeed become undead and move.
Then why didn't he turn when Clem looked at him when carrying nails?
Clementine only observed him a few moments after death. Give it time.
Other characters have turned rather quickly.
Well... Maybe if Reggie's skull was quite badly damaged then turning might take longer.