Continuity mistake: In this episode Leonard has a snoring problem (a result of a deviated septum, which in all probability he was born with, plus Amy says Sheldon has always complained about Leonard's snoring, and Sheldon says after 5 or 6 years he's gotten use to Leonard's snoring), but in episode 14 of season 3 when Sheldon brings up snoring Penny says, "Leonard doesn't snore." And in episode 8 of season 6, Sheldon lists not snoring as one of Leonard's positive traits.
The Troll Manifestation - S8-E14
Continuity mistake: When the gang and Stephen Hawking are video chatting, the Android mascot is lying down when the camera is facing the gang, but when the camera is facing Stephen Hawking, the Android mascot is standing up.
The Comic Book Store Regeneration - S8-E15
Continuity mistake: While in Penny's apartment, Sheldon is folding laundry and Penny is talking to him from the kitchen counter. Between shots, the water bottle in front of Penny moves by itself to different spots on the counter.
The Comic Book Store Regeneration - S8-E15
Continuity mistake: While Bernadette is talking with Howard about Stuart living in Mrs. Walowitz's home, she is taking items out of a grocery bag. One of the bags of food changes spots on the table in the next shot.
The Matrimonial Momentum - S9-E1
Continuity mistake: In the first half of the episode while in Las Vegas, Penny's hair is short; however, later in the episode when she is back in the apartment speaking with Sheldon, her hair is much longer, albeit tied back in a bun, but very obviously much longer and a very different color. The scene from Las Vegas to her apartment was less than 24 hours apart and would have been impossible for her hair to have grown so much.
The Separation Oscillation - S9-E2
Continuity mistake: Sheldon is returning Amy's scarf and says, "You wore it the night we went ice skating, remember?" to which Amy replies, "You mean the night that I went ice skating and you stood at the rail Googling the symptoms of hypothermia." But in episode 8-12: The Space Probe Disintegration, Amy states that she cannot go ice skating because she has "unnaturally brittle ankles." (00:04:55)
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.
The Dependence Transcendence - S10-E3
Continuity mistake: Bernadette is talking to Raj's dad on the video phone. In the close up, her fingers are wrapped round the phone but in the long shot, she is holding her fingers behind it and balancing it with her thumb.
The Fetal Kick Catalyst - S10-E6
Continuity mistake: Near the end of the episode where Sheldon and Stuart are drunk and talking about how Sheldon never leaves the house without a paperclip, the amount of Mimosa in their glasses suddenly decreases between shots.
The Brain Bowl Incubation - S10-E8
Continuity mistake: When Raj puts down the rubber gloves when talking with Isabella, the gloves completely vanish 6 shots later with nobody touching them.
The Escape Hatch Identification - S10-E18
Continuity mistake: Stewart eats a ham sandwich when he and Raj are talking alone in Howard's and Bernadette's living room. On at least one occasion the sandwich's size gets larger, not smaller between bites as Stewart is eating it.
The Recollection Dissipation - S10-E20
Continuity mistake: When Howard and Bernadette are talking in the kitchen by themselves, Howard's bottle of water keeps moving between shots.
The Long Distance Dissonance - S10-E24
Continuity mistake: After the 'Ramona' conversation between Sheldon and Penny ends, Sheldon leaves Penny alone on the couch. Penny looks up to the "Amy and Penny" painting and says "Don't look at me like that, I tried." In S10 E10, Amy gave the painting back to Penny, which was hung in Leonard's living room.
The Long Distance Dissonance - S10-E24
Continuity mistake: When Sheldon takes a plane to see Amy in Princeton, the plane he is on has 2 engines when it takes off and 4 engines when it lands. It's a direct flight from LAX so he wouldn't have changed planes.
The Proposal Proposal - S11-E1
Continuity mistake: When Penny and Bernadette are talking in the kitchen, the string for the teabag in Bernadette's yellow mug keeps moving between shots.
The Retraction Reaction - S11-E2
Continuity mistake: Sheldon's formulae are written on three whiteboards. The marker color on the leftmost board is first red, later black. (00:07:05 - 00:09:21)
The Bow Tie Asymmetry - S11-E24
Continuity mistake: After the ceremony, as Amy and Sheldon are walking down the aisle, different camera angles show Barry Kripke holding the microphone in different hands but without changing them as he is singing.
The Imitation Perturbation - S12-E6
Continuity mistake: When Bernadette and Amy are sitting in the kitchen, the teabag in Bernadette's cup changes position between shots.
The Consummation Deviation - S12-E8
Continuity mistake: Leonard tells Raj that the first sex between Penny and Leonard was fantastic. But episode S3E2 is all about how bad it was.