The Curious Tale of Mr Spearfish - S3-E1
Character mistake: The whole mystery kicks off when Creek sees a photograph of Alice Spearfish with her parents, and concludes that she is adopted because two people with brown eyes cannot have a child with blue eyes. An obsessive polymath like Creek must surely know that that is wrong. The genetics are complex and though uncommon it is possible for a couple with brown eyes to have a child with blue eyes and the other way around.
Plot hole: SPOILER ALERT Louise Bergman murders her father Marco, who is blind, by making a tape of the sound effects of a blazing fire along with her voice urging him to jump to safety out of his upper floor window. A man who has been blind for two years would have learned to rely on his other senses, and would immediately suspect something was wrong - he would feel no heat from the fire nor smell smoke.
Plot hole: The entire plot hinges on Jonathan's solution of the murder of the first wife of Stephen Belkin. That work had the effect of exonerating Belkin. But, Jonathan's solution wouldn't exonerate Belkin in the slightest. It only explained how the murder was accomplished. It did not eliminate Belkin as a suspect. Even after Creek's solution, Belkin still had means, motive and opportunity. As the only surviving person in the locked room where the murder happened, Belkin would have remained the most obvious suspect. In fact, Creek's solution tended to show that only Belkin could have done it, precisely because the room was indeed locked - Creek never explained how a third person could have got in and set up the killing. but in the transmitted episode, it only occurs to Creek much later that, duh, of course Belkin did it.
Continuity mistake: Hugo puts his mug down on the table before going to fetch a book. As turns back from the shelf, the mug is back in his hand, and then as he crosses the room, it is gone again. (00:35:55)
Deliberate mistake: When Joey and Jonathan get in Joey's car at Metropolis (just before heading to the police station), the car has headrests. When they get to the police station, see Lance Gessler leaving and then follow him, the car no longer has headrests. Obviously removed so as not to obstruct the actors.
Plot hole: How did the guy who stalked Emma Lazarus managed to get the box containing her head on the aeroplane without it being checked by airport security? As airline passengers are required to have their personal belongings on them scanned, this should have been detected by the airport security scanner and security staff would have detained the passenger or even arrested him before he had the chance to board the plane.
Plot hole: In the end, we see that Francesca entered the bedroom, ruffed up the bed, and tied herself up before shooting Shale. However, if Katrina hadn't entered the bedroom moments after the fatal shooting, where is Francesca's alibi? If Katrina weren't there, Francesca would have been sat there for possibly hours. The police would reasonably guess she shot him and then tied herself up. How did Francesca know that Katrina was going to be there and at what time in order to testify to her innocence? (00:41:00)
Suggested correction: Jonathan actually states it's a photo of 2 blue eyed parents and a brown eyed daughter.
Which is still possible! It isn't even uncommon. Brown eyed parents can have a blue eyed child and vice versa - that's what recessive genes are all about.