In one of the stock footage shots of the Squad 51 truck in traffic, an older version of the truck is seen, not the one being used by the show at that time.
While transporting the cardiac victim on the engine after defibrillation, Roy injects something WITHOUT contacting Rampart.
Toward the end, when Roy and Johnny are eating at Rampart, they get called on a run to "3882 Market Street, time out 8:20", which is a strange time to be eating burgers. Subsequently they are shown returning exhausted to the station and handling the squad over to the next shift, who then get called on the exact same run (valid plot point) at the exact same time (mistake): "3882 Market Street, time out 8:20".
A little over half way through the show, Squad 51 is responding to a call and is asked for an ETA. Gage looks at his watch and replies "Two minutes." Why look at the watch? The ETA is two minutes regardless of the time.
When the squad responds to a man unconscious call the dispatcher states the time as 14:53, and the shadow of the squad as it leaves the station indicates early afternoon. However, when they arrive at the scene it is almost dark, indicating it took them many hours to get there. Minutes later they respond to another call, and it is afternoon again.
When Roy and Johnny are working on the heart-attack victim, Early instructs Roy to give the victim a dose of "Lidograin Bolus" when the actual medication is called Lidocaine. Two seconds later, Early uses the proper word.