When J. Nathaniel Pierce is talking to Martin in his office, he is holding a set of handcuffs in his right hand. Next shot he is holding the handcuffs with both hands.
When Martin makes himself invisible when Mrs Brown is peeking through the window, the book he is reading is suspended in mid-air. When viewing from Mrs Brown's POV outside, the book can't be seen. When Tim comes home, the book is back in view suspended in mid-air again.
Near the end of the episode, Martin remarks that Mrs. Brown becomes involved in matters like taking a correspondence school's detective course because "Mrs. Brown has no family." This contradicts what was shown in earlier episodes of this season, such as the pilot episode, which introduced both her daughter Angela (Ann Marshall) who also appeared in two other episodes, and her niece
Annabelle (Ina Victor).