Factual error: When the police lieutenant is stabbed to death by the jewellery thief, the case would then fall under homicide, not hostage negotiation. So, the detective nor Murphy would have no authorisation whatsoever to work a homicide case, which is not their unit. Total fiction.
Factual error: I seriously doubt that any police detective would single-handedly go and question any suspects alone. By themselves, at least two or three officers will be present when going to any address of a suspect for questioning, in case of a dangerous encounter.