Plot hole: As Roy and the stagehand are bringing in the equipment to treat the shock victim Engine 51 rolls into the scene. Not enough time has passed for the engine to respond. They haven't even started treating the victim yet.
Other mistake: As the fire apparatus are leaving the station for the helicopter rescue, the shot from the front shows doors at the back of the building but when they are leaving it shows a brick wall at the back of the building.
Other mistake: Stoker prematurely plots 617 Kimble Road on the map as the dispatcher is barely starting to say the address. Then the squad leads in the departure from the station, but when the squad arrives to the above dispatched location the engine is already finished with the dumpster fire.
Other mistake: When the plane crashes into the neighborhood and traps Gage and DeSoto in the house, you see outside shots of the squad when the other two paramedics arrive. You can see a large piece of smoking engine/plane laying on the back end of the squad, right over the spare air tanks. They would have exploded when something that heavy and hot landed on them, since they are filled with oxygen. The tanks would be full or they would not be on the back of the squad.