In the beginning of the film where the credits were being rolled along with the New York Skyline, The World Financial Center did exist in the year 1986, but much of the commercial complex was under construction as well as Battery Park City. Two World Financial Center (the building with the round dome rooftop) was under construction at that year and didn't finish completion until 1987; one year after the time setting.
When the CMB is taking over the Carter Projects by force, the man who gets shot by an Uzi-toting thug while defending his family has holes and blood on his back before the sound of the gunfire is heard.
Just after Scotty are being talked into having Nick in his team, Nick fires his gun creating a pattern of a smiley face onto the wall - but only six shots are heard being fired, and the smiley consists of seven holes.
No cop would show up to testify at a trial with sunglasses on and put his feet up on the front of the witness stand, as Scotty does in the closing court scenes. Officers who testify are instructed to come in suits and don't sit like they're in their basement watching TV.
When Kareem takes Pookie to talk to Gee Money about a promotion, the camera cuts between being in the room and looking through the wire that Pookie is wearing. Gee Money is on the phone during this exchange and his hands switch positions wildly between the shots.
When the train hits the cyclist, the approaching train changes back and forth between a 1960s Multiple Unit electric train set with manually operated doors and a 1970s M2 Cosmopolitan train set with powered sliding doors.
When Needles comes to the club on New Years Eve, Nino pulls a knife and cuts off Needles ponytail. The ponytail comes loose an inch above the blade of the knife when Nino pulls on the ponytail before he moves the blade.
In the beginning of the movie Pooky is riding away on a bike. When he is riding down the stairs you can see that it is not the same bike. The handlebars are different. As he starts off it is a straight bar, when going down the stairs it is lower and has a pad on the cross bar.
During the wedding scene, the two cops break into Nino's safe to steal computer discs. Any evidence gained directly or indirectly from these would be tossed out of court as inadmissible as the result of a (blatantly) illegal search, under the 4th Amendment.
Pookie's time inside the Carter was extensively videotaped, and those tapes, which included G Money giving the order to kill Pookie after his cover is blown, were all saved by the cops. Despite all that taped evidence that could be used to either convict G Money and several others and/or flip them as witnesses against Nino, the operation is declared a total failure and the tapes are never used.
At the beginning of the movie, while coming up to the bridge you can hear the news report that Don Armeteo has been gunned down along with other members of his crew. That does not happen until much later in the movie.