After her sentencing and receiving ten years in prison, Genevieve is taken away in handcuffs and chains via the front door for the viewing public and attorneys. In actuality, if a defendant is detained after the verdict, they are taken away via the service corridor used by correctional officers and defendants brought from jail.
The Vulture is wearing his American Flag bar out of order. NYPD regulations require that it be worn as the highest citation bar. Not that the Vulture would ever care.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
After threatening to poison Hitchcock and Scully, Rosa says she will, "tell their widows they were thieves." It is well known that Hitchcock is a multiple divorcee, and Rosa was present in The Funeral (2015) when Scully received a text from his wife stating that she was leaving him.
Jake is surprised to find that Charles is not upset that the woman he likes was sentenced to 10 years in "jail." Jail is where people are held awaiting trial or for minor sentences (typically less than 1 year). Someone serving a 10 year sentence would be sent to a prison, not a jail.