Continuity mistake: When Murdoch and Crabtree arrive to the fairground to apprehend Agnes, they lean their bikes against the "annual fair" banner stretched on a handrail. The camera shows the detective and the constable from behind, making visible that the weight of the bikes make the banner to ruck down significantly. However, when the next cut shows them frontwise, the banner is in neutral position. (00:40:30)
Continuity mistake: Shortly after arriving to the crime scene, Murdoch instructs Crabtree to collect the fingerprints of the asylum patients - but the women in the institute were arrested before (most of them by Murdoch himself) so their fingerprints should've been collected already. It's pointless collecting them again.
Bend It Like Brackenreid - S10-E7
Continuity mistake: At the beginning of the episode, some of the main characters are spectating the ongoing football match. Look at Dr. Ogden: the position of her hands - therefore the way she is holding her bag - keep changing cut by cut.
Character mistake: It's more than unlikely that a prison guard would leave a suspected murderer (George) alone with anyone, especially a woman (Edna) for minutes. (00:24:28)
Glory Days - S8-E3
Continuity mistake: Towards the end of the episode, during the final shootout, Murdoch ambushes an armed bad guy in the attic and jumps through the wooden wall with him. As they fall down, Murdoch's trademark hat spectacularly flies off his head, but in the next overhead cut - showing him and the bad guy lying on the ground - the hat is on his head again.
