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.
Character mistake: When the zombies break into Buffy's house, she stakes one to check if it's a vampire. But she should know full well that it isn't a vampire as they all broke into her house without being invited.
Gentleman Thief's Murder: File 3 - S1-E12
Character mistake: Itsuki tells Kindaichi about the painting the strange man was doing, saying it was "My Beloved Daughter." That is incorrect though, since what Itsuki would have been able to gather from the hospital staff was that the man painted lavender fields literally all over the room. The staff would remember that (a whole room of the building was changed!) and not that specific painting - and if they knew about it, news of it would have spread, being one of the most famous paintings in the world.
Character mistake: When Walker and Satch are in the car looking for Walker's son, Walker tells Satch his son is 17. Afterward, when they are out on the streets, Walker asks some people if they have seen his 18-year old son.
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.