In the ambush scene where assassins hit the car Mr Reese was driving, this results in an accident where he hits his head on the wheel and passes out. Five seconds later, he's already up and fighting the assassins like the whole thing didn't happen at all.
The same woman walks by Peck twice when he and Finch are talking. She is carrying a black bag and has a brown cuff on her jacket.
There is no explanation as to how Mr. Reese found Mr. Finch's address. He just "happens" to find it.
When Reese mentions to Finch that their person of interest works in a SCIF, the next shot shows Finch looking up "Secure Compartmented Information Facility" on the internet. Given Finch's background with the NSA, information security, and classified data, there is no way he'd need to look that up.