When Lamble climbs onto the window ledge of his hospital room we are shown that it is meant to be many storeys high, with a grey and overcast vista far below. In the supposed reverse shot, we can see the shadow of a tree's leaves falling on Lamble. The building would be far too high for a tree to be anywhere near the same height as Lamble's room and the murky weather apparent in the filmed vista would not allow the casting of strong shadows.
During Mrs Peel's initiation test, her metal contact clearly touches the electrified metal rail when the first seesaw teeters under her feet ... but she isn't electrocuted, nor does the alarm bell sound.
Just before they ride off in the end scene, Steed gives a long speech to Mrs Peel with a string of names in it. Rather than look at her, his eyes move side to side - he's obviously reading the line rather than having learned it.
In the scene where Steed is carefully opening Emma's box of chocolates, a crew member's arm is visible.