The Daughters of Jerusalem - S2-E6
Plot hole: Dinah Fortescue's fingerprints are supposed to be on a teacup but she's wearing gloves in the flashback. So how did they get there? (00:24:35 - 00:33:34)
The Curse of the Aesthetic - S8-E8
Continuity mistake: When the nanny is found dead, the ball of wool in the bag is yellow but later on when Father Brown picks up the wool out of the bag it is grey.