Around 35:45 into the movie, when Darryl and Sean sit on the couch under which Becky hides, the window is open only a few inches. But after their conversation, at 41:17, Darryl stands up to close that window, and it is wide open.
At the 1h12m mark, after Becky has killed her, the old lady is shown laying face down on the floor. At 1h12m12s, she is shown laying on her side. And at 1h12m21s, she is shown face down, again.
In the end, the CIA would normally have nothing to do with domestic terrorism, this is the domain of the FBI or DHS. The coordinates on the key, however, are somewhere in Europe, which points to an international plot to be revealed in the next sequel.
When Daryl realizes that the pin had been pulled from the grenade in Anthony's mouth, he quickly slams the door shut but watches the explosion through the widow in the door. If Daryl really had as much time in the military he would have known that neither the door nor the window would provide enough protection against a fragmentation grenade at such close range and he would have instead taken cover behind a wall.
While she is waiting to finish her shift at the diner, the camera focuses on the clock on the wall and you hear the tick, tick, tick until she clocks out. The clock had a sweep second hand = no ticking sound.
When Becky takes out Darryl Sr and Darryl Jr is coming out of the bathroom after being blinded, she runs past the loaded gun that she could have picked up to kill Darryl Jr, with. Instead, she puts her life further at risk being chased and shot at by Darryl Jr. who does meet his end another way.
Becky arranges the word ANEW with her tiles during the scrabble game. She then plays the four letters and states that her word is ANEW. As this wasn't the first word of the game, she would have to have attached it to at least one other letter, either as an extension to another word (in which case the new word would not be ANEW) or perpendicular to another letter, in which case another word would have been made, which would have resulted in an additional word score, which she did not acknowledge.