The Mexican cartel is referred to as 'Mano Sangriento', this is a mistake as in Spanish the word Mano (Hand) is a feminine term, and therefore Sangriento should also be used in its feminine form, Sangrienta.
When Jamie is leading to the victims in the alley, the woman playing the deceased female victim blinks throughout the three shots she is in.
During the gunfight with the cartel. Baez is shooting, the weapon is pointing at about 15% degrees toward the sky. Clearly not aiming.
When the Mayor is talking to Frank after Danny's house burned down, he moves his legs slightly when facing the window. In the next scene, when facing Frank, his left leg muscles twitch.
When Danny's house is burning, the radio call said "NYFD" was on scene. In reality, the fire department always is referred to as FDNY.