Throughout the series, the large black-and-white rose tattoo on the back of Miguel's hand alternates between being on his right hand and on his left.
Prisoners are often seen using knives and scissors as regular every day items (getting haircuts etc). Access to metal bladed instruments would not be allowed in any form without strict supervision. Every pair of scissors and every knife would accounted for at all times.
Throughout the series when inmates are murdered, or die under suspicious circumstances, the corrections officers are shown coming and removing the body without even documenting anything, and the homicide investigated by the Warden and prison staff, and occasionally the police. Which is totally inaccurate, when a prison inmate is murdered or dies under suspicious circumstances it is investigated in exactly the same manner as any homicide is. The area where the inmate was killed, like their cell, would be treated as a crime scene, and it would not be processed or investigated by prison staff. Homicides committed in state prisons are investigated by the state police, and in federal prisons by the FBI, the only thing the guards would do is preserve the crime scene until the police/feds arrived. They are not allowed to touch or remove anything, especially the body, until the proper authorities and the medical examiner have arrived and documented the crime scene.
The detectives investigating crimes committed in Oz are always shown wearing NYPD badges, which is incorrect. Oz is a New York state correctional facility, and any crimes committed inside a state prison fall under the jurisdiction of the New York State Police, so the detectives investigating a murder in Oz would be state police detectives. (their badge looks nothing like an NYPD badge). Even if a state prison is located inside a city the State Police still have jurisdiction inside the walls. The only correctional facility the NYPD has jurisdiction over is Riker's Island, as that is a city jail.