When Henry finally returns to his apartment, a little before finding out Marty's having a baby, the street he's walking seems wet as if it rained the whole day. However, during the whole movie the weather was very sunny.
The shooting incident occurred in Brooklyn's (fictional) 91st Precinct in the Williamsburg section, yet the two suspects are "perp walked" from 100 Centre Street, which is the Manhattan Criminal Courts. In reality, these suspects would have been processed at Brooklyn's central booking facility at 120 Schermerhorn Street, and walked IN to the building, where they would be arraigned, not OUT.
When Henry tries to "Stop the presses", they have to find "Chuck" to unlock the stop button... this is totally wrong; on presses like this, there are stop buttons everywhere, and ANYONE can stop the press (although they'd better have a good reason for doing so)... what if someone were caught in the press, they're going to take 10 minutes to find the guy with the key to unlock the stop button? No way...
One of the boys is 19, the other 17, a minor. They would not have been placed in the same detention cell together overnight, in fact its unlikely they would have even been arraigned in the same court. Nor would the minor have likely been perp-walked in front of the press.