After Manny is fingerprinted, he wipes his inked hands off on a paper towel but much of the ink stays on his fingers. He is shown looking at his hands in the jail cell a few shots afterwards and his fingers are completely clean even though he never washed them in between walking to the jail cell and while inside the cell.
Christopher Balestrero is called "Chris" by the police until they get him to the precinct and start parading him around the town to be identified. When they get back to the precinct, they begin calling him "Manny". I don't think that there is any time when the police are advised of his preference to be called Manny.
The police truck Manny is loaded into to take him to Long Island jail has the number 1437 painted on it. The next shot shows the police truck crossing a bridge with the number 1403 visible on it. When it arrives at the jail it again has the number 1437 on it.
Twice when Manny enters the house we are presumed to believe that he has left the door open. The first time he enters he makes a slight closing motion but nothing happens and the second time a door is heard closing, yet because of the camera position it is presumed that it couldn't be possible to close the door.