It is morning time when Holmes realizes what Mrs. Purcell was doing with her secret video tapes (having stayed up all night watching the endless hours of video) and calls Capt. Gregson to immediately arrest Mr. Purcell. However, when they arrive at his house to arrest him it is night time.
When rationalizing his messiness in a conversation with Watson, Sherlock erroneously attributes the discovery of penicillin to Andrew Fleming, rather than its actual discoverer Alexander Fleming.