Since the inception of the agency, FBI agents travel in pairs when interview subjects. This is both to have a witness to the interview as well as for protection in case unexpected things occur.
Multiple times during the show, single agents are shown talking with subjects alone, even in their homes or places unfamiliar to the agents.
In more than one instance, suspects being interviewed with a polygraph answer all the control questions (Is your name John Doe? Are you 39?) truthfully. In reality, a suspect is told to answer all the control questions "yes", whether true or not, to determine the accuracy of the polygraph machine.
There is no FBI unit tasked with looking for kidnapping victims in the manner shown in the series. Besides many of the offenses shown being state, rather than federal, cases, it would take at least several days for the FBI to become full involved in most kidnappings, primarily due to jurisdictional issues.
The real FBI does investigate missing persons; as needed but they do not have a dedicated Missing Persons Unit as portrayed in the show.
There are a number of scenes which indicate that the show is actually shot in Los Angeles and not New York, where the show is supposed to take place. There are several supposed one way streets with double yellow lines painted down the middle (which do not exist in New York), large blue street signs (which are used in LA, as opposed to NY, which uses green street signs), and house numbers on each street painted into the sidewalk in front of each house, which is also not done in New York, but instead in Los Angeles.