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.
Chosen answer: It does. The variable cleanliness of the cab and the habit of taxi drivers to engage customers in small talk would be too much for Sheldon to handle, and not an option for him.
Captain Defenestrator