The homicide of an NYPD detective, especially one involved in a mob case, would not be handled by precinct detectives like Danny and Baez. It would be handled by the Major Case squad. Danny's position appears to be in a precinct in certain episodes, but in Major Case in others (such as Season 8, Episode 8, where he picks up the phone and announces himself as "Detective Reagan, Major Case").
When Jimmy walks up to the bar with his girlfriend towards the end of the story. There is a man with a beer sitting next to him. As he buys beers for the bar, an arm and shoulder can be seen to Jimmy's right. When the camera angle changes. Anthony is now sitting in that seat. That change would not happen that fast in real life, and there was no sign of Anthony before the change.
When Jimmy drives into Carlo's chop shop the compound gate is wide open and there is no one in the compound to close it, and it isn't a remote controlled gate. But moments later as Jimmy makes the sell, the police race in busting through the gate, which was closed.
Danny is questioning Victor Lugo in the barbershop and Danny grabs him by the neck. Once Danny releases Victor he notices the cut on his neck they cut away and you see shaving cream all around Victor's mouth. The next shot the cream is missing on the right side, the following shot all the shaving cream is back around Victor's mouth.
Garrett as a high level NYPD employee would be well known, especially by the "small department" where he lives. Even if he were not, police procedure is to make contact with a suspect. This would be attempted by phone or by bullhorn. The police would not wait for someone to come outside as was shown. Accordingly, the takedown of Garret and his wife would never have taken place.