Continuity mistake: Mr. Giles holds the telephone as he interrogates the private eye, who answers in a rather defiant way to the threat of "the local constable" getting involved. So Giles puts the receiver down, but notice that in the first shot he is passing it from the right to the left hand. In the close-up it is the right hand to hang up, though. (00:23:15)
Continuity mistake: During the scene at the train station, Jessica's nephew introduces to her Kitt Donovan from the publishing company. Just as he says "in public relations", a man pops in the foreground - it is an extra that walks out of the rail car. In the reverse shot that follows, the same extra is only then coming out of the train. (00:09:35)
Continuity mistake: Episode 1-0, "The Murder of Sherlock Holmes"; Mr. Giles opens the door of the antechamber of his office, finally putting an end to Jessica's long wait. Grady right away at the first click of the lock takes his hands off his pockets and tidies up his sleeves. But in the next shot when Grady actually enters and talks to the secretary, Grady is still with his hands on his pockets repeating the gesture. (00:10:10)
Continuity mistake: When the character played by Ron Moody runs into the sea in pursuit of a suspect trying to escape, he shouts at Jessica to "Get the package!" In the next shot we see Jessica reluctantly follow him in, with a clear waterline from a previous take showing on her dark overcoat/cloak.