As a patient and potential suspect, Delko should not have been allowed to investigate the daughter's murder, as his fingerprints, hair and other DNA would have been found around the crime scene.
The medical examiner is shown cutting into the doctor's back to retrieve the bullet that killed her at the crime scene. In real life, the bullet would have been removed back at the coroner's office during the autopsy.
Eric and Calleigh are shown looking through patient files without a search warrant. The police are only allowed to view a patient's file after they have already established that they are a suspect and have supporting evidence. They are never allowed to just troll through every file looking for a possible suspect. Eric and Calleigh's actions would open them up to invasion of privacy lawsuits from every patient whose file they read.
Dolly track visible on the boat's reflection while camera pans down the boat before Shane Huntington gets arrested.