The Platonic Permutation - S9-E9
Continuity mistake: In episode 16 of season 1, Penny is talking about making a cake for Leonard's birthday and states she knows his birthday because she was checking a horoscope for him. But in this episode she does not know when his birthday is, which leads to Leonard revealing he was secretly reading Penny's diary. (00:40:00)
Suggested correction: It's certainly possible to forget something you knew eight years ago.
This is perhaps true for two people who rarely have contact, but I would list this as a character mistake. Penny and Leonard are in a serious relationship and are married at this point.
This is also a couple who BOTH forgot it was their anniversary.
I forgot my wife's birthday on a number of occasions. It's one of the reasons she is now my ex-wife.
There's a difference between forgetting and not knowing.