The Girl on the Balance Beam - S5-E18
Other mistake: Twice during this episode, when they're dispatched to a "woman trapped on a wire" and also to the "train fire", we see Engine 51 heading out with two firemen standing at the back of the engine, and they are Johnny and Roy. This footage is actually from the episode "The Old Engine" in season 3, when they got the new Ward La France engine for Station 51, and since Roy and Johnny were waiting for the previous shift to return with the squad, Captain Stanley told them to jump on the back and go with them on their first run with the new engine.