Just about everything related to inmate security in Rikers Island and court holding cells is wrong. As an accused murderer, Khan would only be out of handcuffs while in a jail cell, he would not be mixed in with inmates charged with lesser crimes, he would absolutely not be led in to a "family funday" visitation meeting with other inmates and their families; he would not be uncuffed during arraignment.
A murder like this sprays blood everywhere (as can be seen in the crime scene) but at no stage does his defense ask for an explanation of why he wasn't covered in her blood.
The asthma inhaler was found on the bed next to the corpse. Despite the large amount of blood splattered everywhere in the bedroom and on bed, the inhaler wasn't covered in blood.
The plot turns on Nasir "borrowing" his father's medallion taxi on a Friday night. Most medallion taxis are not parked on the street overnight, and Friday night is peak time for NYC taxis - it did not make sense for it to be out of service.