The Cooper Extraction - S7-E11
Continuity mistake: When Amy says that Penny never would have met Stan Lee, she draws a thick black line between "Penny" and "Stan Lee" on the board. The camera goes to Penny, and when it comes back to Amy, the line is blue and faint.
The Convention Conundrum - S7-E14
Character mistake: On Sheldon's board of possible attendees for his convention he has misspelled Ian McKellen - with 'an' at the end.
The Locomotive Manipulation - S7-E15
Continuity mistake: At the end of the episode when Lennard asks Sheldon about his train ride, he says that he kissed Amy on the lips, and says that it tasted like the brownies that they had that for dessert. But they were eating a tart of some type, with a shortbread crust. No brownies were on the table.
The Mommy Observation - S7-E18
Factual error: Based on the length of Bernadette's skirt and the place she's standing, Stuart could never see under it.
The Gorilla Dissolution - S7-E23
Revealing mistake: After Howard lets go of the unpacked treadmill, it begins to fall down the stairs. As it goes out of frame, the treadmill begins to level itself out, but the sound of it is still heard falling and Howard, Bernadette and Raj continue running past, way further than where it levelled itself out anyway. (00:00:35)
The Junior Professor Solution - S8-E2
Character mistake: When Howard is asking Sheldon engineering questions, the first question is "How do you quantify the strength of materials?" Sheldon answers "Young's Modulus," and Howard admits that is correct. But it's not correct - Young's Modulus quantifies a material's elasticity, not strength. (00:17:10)
The First Pitch Insufficiency - S8-E3
Continuity mistake: When Howard is on the mound, the shot from behind the plate shows a player ready to catch the ball in a uniform shirt. The next long shot from the stands shows a catcher in full gear, and then back to behind the plate to the player in uniform shirt only.
Other mistake: Leonard says he had a growth spurt after his high school prom. In "The Cooper-Hofstadter Polarization" he told Penny that he still had all his clothes he owned since the eighth grade, after his last growth spurt.
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 Clean Room Infiltration - S8-E11
Other mistake: When Howard, Leonard, and Raj are arguing in the clean room, Howard says that Leonard is jealous because Howard and Leonard used to be "best friends until Koothrapali came along." Yet, in the earlier seasons, we know that Howard and Raj already knew each other when Leonard met them for the first time and brought them back to the apartment to play video games. Meaning they couldn't have been best friends before Raj came along.
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 Colonization Application - S8-E17
Character mistake: Leonard and Penny were using the body paint the second time, the entire canvas is covered, and they each are covered with paint. But not a bit got into their hair.
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 2003 Approximation - S9-E4
Factual error: Sheldon tries to pretend that it is 2003, before he met Leonard. But in the episode The 21 Second Excitation S4 E8 it was stated Leonard and Sheldon waited in line for 14 hours to see the midnight premiere of Star Trek: Nemesis. Star Trek: Nemesis premiered on the 9th of December 2002.
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 Convergence Convergence - S9-E24
Other mistake: Howard believes he's being followed by the government, when it's actually Leonard, Penny, and Beverly in their car. The shots from Howard's car show only Leonard's silhouette. The other two do not appear as silhouettes.
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.