After Emma bolts the door from the inside, the door is seen opening slightly as the attacker claws from the outside.
When Sir Lexius Cray whistles in his bird of prey, Emma watches a peregrine falcon fly in, but when it alights on Cray's arm it is a Harris hawk.
The Winged Avenger climbs various different buildings to get at his victims, but the outside of each building is exactly the same set.
When the Winged Avenger is hanging upside down on the ceiling, his cape is still hanging down his shoulders instead of facing the other way.
When Mrs. Peel is fighting the Winged Avenger, a chair is dislodged from Professor Poole's ceiling-mounted office. The chair wobbles in mid-air on its way down, indicating that it is, in fact, being pulled upwards by a wire.
The strap hanging from the upside-down Mrs. Peel's outfit is stiff, clearly indicating that it is a prop attached to make it look like she was upside-down, when she really was standing upright on a ceiling set.