When Steed and Mrs Peel investigate the first death (Cosgrove) he had been taking photographs. Steed has them and Mrs Peel says they are fogged. Having taken the time to develop and print the photos and deliver to Steed in the observatory, Cosgroves body is still on the floor.
It's impossible to see stars in the same telescopic field of view as Venus. Its brightness drowns them out completely.
Venus can never be seen as a complete disc since it's closer to the Sun than the Earth. The closest it comes to this is when it's in the gibbous phase, but even then it's not a circle.
Lasers do not make any sound.
When Steed's car arrives at the villain's lair, only 1 headlight is lit.
Dr. Primble's profession is misspelled on the light outside his door. It should be 'ophthalmic surgeon', not 'opthalmic surgeon'.
Since the lethal laser device was mounted on the hood (bonnet) of the car facing forward, and Emma was able to follow the light when it left a targeted hit, that would mean its operator was driving in reverse throughout the lengthy getaway on narrow, winding country roads.
When Steed is playing the tape for Mrs. Peel the volume control was at "0" so it would not be possible for any sound to be heard.
When Mansford was found dead inside his safe, his eyelids could be seen moving.