And Justice For All… - S1-E10
Factual error: One of the cops confirms at the end of the episode in the vault that the fingerprints on the gun match Prater's fingerprints. Far too little time has elapsed in between the body/gun being discovered and her saying this for this to be possible. Lifting fingerprints off a gun isn't simple or quick to do, and would be done in a lab, which hasn't happened. Even assuming the NYPD expedited everything given the high-profile case, there's no way this would all be done in under half an hour.
Suggested correction: They don't use water as a coolant, but they can collect water that condensed from the cold inside the unit.
LorgSkyegon
Which still doesn't allow for legionella to breed, not least the limited amount of collected water drains away (i.e. not like in water tanks and cooling towers). Healthcare professionals have consistently confirmed that window AC units aren't legionella risks for this reason. If you check the CDC website, it explicitly states that window AC units aren't potential legionella sources.