The Staircase Implementation - S3-E22
Character mistake: In 1-14 "The Nerdvana Annihilation", when Howard says they should put the time machine into the elevator, Leonard states the elevator had been broken for two years. But in this episode, we found out the elevator broke seven years earlier. (00:03:10)
The Cruciferous Vegetable Amplification - S4-E2
Character mistake: In the first scene, on Sheldon's board are the words "D-D Fushion." This should be fusion. Sheldon wouldn't make a mistake like that.
The Justice League Recombination - S4-E11
Character mistake: Even with Penny and Zack the guys are one man short to be the original JLA because they they don't have the Martian Manhunter. If they used the same costumes in the previous year, they would have been three people short of the original line-up.
The Cohabitation Formulation - S4-E16
Character mistake: When Penny says she smells Chinese food and Sheldon corrects her by telling her she's slipping because it's Thai, Sheldon is eating the food with chopsticks, even though in a previous episode he uses a fork and spoon because that's how Thai people eat their food. (00:19:15)
The Zarnecki Incursion - S4-E19
Character mistake: As they drive to Todd Zarnecki's to confront him, Sheldon says, "I almost feel sorry for the poor fool, sitting in his split-level suburban ranch..." Architecturally, split-level (technically three levels joined by half flights of stairs) and ranch (single level) are separate and distinct designs. There is no "fusion" of the two. I can't help but think Sheldon would have corrected anyone who said the same thing.
Suggested correction: Actually the term "split level ranch" is used to describe a house that has one full floor above ground and a partial lower level, vs the traditional split level house which has a full floor above ground, a second partial floor and a partial lower level.
The Russian Rocket Reaction - S5-E5
Character mistake: Sheldon says he drove for hours in a bus to meet Wil Wheaton. He meant he rode on a bus. Sheldon never would've made that semantic error.
The Speckerman Recurrence - S5-E11
Character mistake: Throughout the show, Sheldon denounced his mother's religion and God. To the extreme. In this episode, he said, "More sense than God gave a mouse." He would never invoke God for any reason.
The Shiny Trinket Maneuver - S5-E12
Character mistake: The bird that Sheldon is afraid of is referred to in the scene as a "Blue Jay." In fact, the bird is a Black-throated Magpie. A Blue Jay is a little smaller, has a shorter tail, does not have the darker plumage, and can be quite obnoxiously vocal.
The Beta Test Initiation - S5-E14
Character mistake: Sheldon says (during Fun With Flags) "But like the flag over Fort Sumter, I'm still here." The Sumter flag was lowered when the fort surrendered to the Confederates. The flag over Fort McHenry was never taken down despite the British bombardment and inspired Francis Scott Key to write the National Anthem about it. Whouldn't a vexologist know that?
Suggested correction: Sheldon is referring to the actual Fort Sumter flag, which still exists and is on display at the Fort Sumter museum.
Sheldon is not referring the actual flag (especially since if the actual flag is in a museum it's not still over Fort Sumter). Sheldon is referencing the line from The Star-Spangled Banner "our flag was still there." Key wrote The Star-Spangled Banner after seeing the flag over Fort McHenry was still there. The writers simply made a mistake and Sheldon the character would know which flag inspired the line. Incidentally, the actual Fort McHenry flag also still exists.
The Friendship Contraction - S5-E15
Character mistake: Sheldon told Leonard at lunch that they were no longer friends, only roommates but later that day, he told start moved up to ninth place on his friends list because he dropped someone (can't remember who) off his friends list). In actuality, it would've bumped him up to eighth place because he kicked Leonard off the list.
The Vacation Solution - S5-E16
Character mistake: In Amy's lab, when she is complaining to Sheldon how she gave him the simplest tasks, and that they're still not done, Sheldon replies with how Einstein failed math because he wasn't challenged, and that it is the same case with him. Einstein never failed math. Sheldon of all characters should know that.
The Werewolf Transformation - S5-E18
Character mistake: In S5-15, Sheldon is asking his friends to take him to SuperCuts. But in this episode, he goes to Mr. D'Onofrio's barber shop where he says he's gone to since he moved to CA, and he said D'Onofrio had his "haircut records."
The Hawking Excitation - S5-E21
Character mistake: The sign on Howard's laboratory door reads "RESTICTED area".
The Cooper/Kripke Inversion - S6-E14
Character mistake: As Leonard is leaving the Mechanical Engineering lab, the sign on the door is spelled incorrectly as 'resticted area' instead of 'restricted area'. (00:04:07)
The Proton Displacement - S7-E7
Character mistake: When Raj shows Penny, Amy, and Bernadette how to make jewelry, Penny keeps having trouble with the glue and gets it all over her fingers. However, in Season 2, episode 5, she has no trouble at all with the glue when making 1000 Penny Blossoms.
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 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 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 Retraction Reaction - S11-E2
Character mistake: When speaking on the radio, Leonard says he has never heard himself through headphones. We have seen him several time wearing headphones while speaking, for example during a podcast with Will Wheaten and on Science Friday too.
The Retraction Reaction - S11-E2
Character mistake: When Leonard arrives at the Human Resources office, he tells the HR person that he's not used to being called into the Dean's office. He's not in the Dean's office, he's in HR.