Others have said some of this already, but this is my two cents:
1. I don't buy Carter betraying Reese to the CIA, after he saved her life and after she made statements to the effect that she dislikes and distrusts them almost as much as Reese does. I think she would have gone to the parking garage by herself.
2. Where was the short assault rifle Reese had earlier in the garage? Did he just drop it and leave it for some kids to find?
3. A competent sniper with a lit-up, stationary target would have either killed him intstantly with a chest or head shot, or if the intent was to disable, would have gone for a knee or a shin. Where he got hit made no sense. A hit in the lower abdomen may or may not disable, but also may or may not kill. Also, Reese is not likely going to be able to walk down a flight of stairs after getting hit in the abdomen with a high-powered rifle.
4. What happened to the CIA guys after the shooting? They started to give chase, then just disappeared, while Carter, Reese and Finch had their whole scene at the car.
I really like the show, but they need to start paying more attention to details.
A bigger question I have is why are they are going to all this effort and taking all these risks to prevent one violent crime at a time in NYC? That is a drop in the bucket! NYC has over 800 murders a year, so are Reese and Finch going to prevent 2-3 a day? How do they prioritize? And are only NYC residents worth saving? What if a Number comes up in Jersey? Or Philly? Do they just ignore those? I would like to see them go nation-wide and have some bigger purpose, like preventing a lot of people from getting killed or taking down big crime rings. If I had the power of "The Machine" that's what I'd do.