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.
Simpsons Already Did It - S6-E7
Character mistake: Butters says that he watched "all 132 episodes" of the Simpsons; at the time this episode aired, 291 episodes of the Simpsons had been produced and aired.
Suggested correction: Butters is always shown as being a bit dim and slow. As a kid it's easy for him to make a mistake in thinking that there was only 132 episodes.
That's why it's called a "character mistake"; also, Butters is certainly naive, but he's hardly what I would call "dim and slow."
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.