NYPD has no authority outside the City of New York, let alone in a different state. Any collection of evidence against anyone in Texas would violate the fruit of the poisonous tree doctrine, and would be inadmissible in a NYC court.
Captain Holt & Terry wear a Commendation breast bar above their World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
Scully is wearing one "fake" commendation bar that is not issued by the NYPD. Also, his black World Trade Center bar should be worn as the highest decoration on his rack.
None of the police officers are wearing mourning bands (black material stretched across the badge) on their badges. When an officer dies, the entire Department wears a mourning band on their badge for a specified period of time. This would be very revealing that an officer had not actually been lost.
The "stage" of Santiago's fake pregnancy suggests she got pregnant in her previous prison or, possibly, during trial while still in jail where there are no alone-time visits. Either way she would have bee granted transfer to a low-security facility and she would not be kept in general population in a maximum security prison by law, regardless of her application.
Gina fills out Pimento's fake death certificate and lists his time of death as 8:26 PM. A corpse fished out of the sewer could not have such a specific time of death, listed down to the minute.