Visible crew/equipment: Robert pushes Ray into accepting his offer to go on a citizen's ride-along. They are initially sitting on the couch at the time, and when they rise, if you look closely behind where Ray is standing, through one of the kitchen windows you can spot a production crew member.
Factual error: Robert's voyeuristic neighbors are using the same elevator as Robert does and tease him about seeing him and Amy through his bedroom window. But if they were able to see into his bedroom, they would not be using that elevator; it would be in another building. From the outside shot of his apartment building, it would be impossible to look into his bedroom.
Continuity mistake: Ray offers to rub Debra's feet instead of doing another chore. He takes her black socks off and throws them on the floor, under the table. The socks can be seen for a few shots, in the same spot, after Robert comes in. At one point, however, one of Debra's black socks can be seen on the couch in the middle, and in the next shot, the sock has been removed.
Factual error: Robert begins as a SGT in the NYPD (later promoted to LT). However, he has issued speeding tickets in his brother's/parent's neighborhood. The family Barone lives in Lynbrook NY. Lynbrook is part of Nassau County, Long Island, which is not part of NYC. Robert would have no jurisdiction to issue speeding tickets there.