When the lights go out and Arthur runs downstairs, when he is unlocking the top bolt you can see another lock under it, but when he has come back and is closing the door against the wind it has disappeared.
When Mr. Kidd is in the nursery for the first time, just before the toy soldier is supposed to magically appear in his hand, you can see the actor reach into his pocket and retrieve said object then conceal it in his palm.
When Arthur Kidd arrives at work at the start of the film, one of the junior clerks mentions seeing Chaplin's The Gold Rush (1925). However, in the later scene where Mrs. Drablow's coffin is lowered into the ground, her name plate on the coffin identifies her as having died in January of 1925. The film was not released in the UK until September of that year.
At 29.45, whilst Arthur Kidd is on the land outside Eel Marsh House. You can briefly see the actress who plays the Woman in Black herself (Pauline Moran) step up from a concealed area behind him, to give the appearance that she has suddenly materialised there.
At 30:00 Kidd is confronted by the ghost of the Woman in Black and flees in terror. Minutes later he discovers a phonograph and amuses himself by recording a joke onto it and playing it back, seemingly unconcerned by what he had just seen.