The Pork Chop Indeterminacy - S1-E15
Character mistake: In his conversation with Missy Sheldon makes it clear that his superior intelligence is a result of a random, mutated gene. Since Missy isn't similarly intelligent she obviously isn't carrying this mutated gene (which would be a billion to one shot anyway) so her offspring wouldn't inherit it. Sheldon would know this - his offspring would carry the mutated gene for superior intelligence, Missy's would not. Anyone knowing enough about genetics to use the term 'randomly mutated gene' understands enough to know that the mutated gene would only be expressed in a direct line from the carrier - Sheldon. Also bear in mind he has a model of the DNA molecule in his living room - it is obviously an interest.
The Big Bran Hypothesis - S1-E2
Character mistake: In his argument with Leonard regarding Superman's ability to fly, Sheldon states that in Superman 1, Lois Lane is two feet off the ground when Superman catches her as she falls from the helicopter. Not so. Superman catches Lois at least ten stories up. Additionally, both Penny and Sheldon say Superman "swoops down" to save Lois. Penny can be forgiven, but Sheldon would know better: Superman flies UP from ground level to catch Lois. (00:02:30)
Character mistake: At the very beginning of the episode Leonard says "So you see what you're eating is not technically yogurt because it doesn't have enough live active acidophilus cultures." He is implying this is a scientific fact (he's not just giving his opinion on yogurt.) But to meet the U.S. standards for yogurt, only the starter cultures Lactobacillus bulgaricus and Streptococcus thermophilus are required, not Lactobacillus acidophilus. The presence or absence of L. acidophilus does NOT determine a food's identity as yogurt (which Leonard's line is implying). (00:00:05)
The Pork Chop Indeterminacy - S1-E15
Character mistake: Through the whole episode, Missy's accent is sometimes completely missing in scenes and then stronger and more noticeable in others.
Character mistake: Sheldon is a well-documented and self-proclaimed germophobe. It is completely out of character for him to retrieve the bag of chicken from the trash.
The Maternal Capacitance - S2-E15
Character mistake: Leonard has his phone on his left ear. Sheldon says "Since ears don't cross hemispheres..." This is an error. The vast majority of the input to the left (or right) ear crosses over to the opposite hemisphere.
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 Excelsior Acquisition - S3-E16
Character mistake: When Howard finds the stack of paychecks in Sheldon's drawer and wonders why Sheldon hasn't cashed them, Sheldon explains that he's saving them to purchase items that have yet to be invented and he doesn't trust banks. But just keeping them in his drawer doesn't do anything, because checks are voided after a set period of time and they would eventually become worthless.
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 Hawking Excitation - S5-E21
Character mistake: The sign on Howard's laboratory door reads "RESTICTED area".
The Hamburger Postulate - S1-E5
Character mistake: Leslie states that heroin causes pupils to dilate, like when Leonard sees Penny. Opiates cause pupils to constrict. (00:06:20)
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)
Character mistake: When Sheldon arrives at the apartment with his Nintendo 64 in the box, he tells Leonard that they can play Super Mario 64. He then proceeds to say, upon finding a memory card, that they can pick up where he left off. Super Mario 64 does not make use of the memory card for progression, all of that data was saved on the cartridge. (00:07:25)
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 Nerdvana Annihilation - S1-E14
Character mistake: Being the first to play in the "time machine," Leonard says he will set the date for March 10, 1876. Howard says "Good choice. Alexander Graham Bell invents the telephone and calls out for Doctor Watson." Bell's assistant, Thomas A. Watson, was an experienced electrical designer and mechanic, but he did not hold an advanced degree. It is well documented that the first words transmitted over the telephone identified him as Mister Watson.
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 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 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 Gothowitz Deviation - S3-E3
Character mistake: Sheldon refers to using the spray bottle as negative reinforcement when it is in fact positive punishment. Reinforcement involves encouraging a behaviour by either adding or removing a stimulus whereas punishment involves discouraging a behaviour by adding or removing a stimulus. Sheldon would know the difference.
The Adhesive Duck Deficiency - S3-E8
Character mistake: When Sheldon is placing his order near the beginning of the episode, he states "In the mid-18th century, King Rama IV of Siam..." King Rama IV was born 18th October 1804 and died 1st October 1868. His reign was during the mid-19th century (1851-1868).
Suggested correction: Genes can be dormant. Which allows them to skip generations. Therefor Missy's children could actually get the "mutated" gene. This is especially true since Sheldon and Missy are twins. Also, since the episode is about who out of Leonard, Howard or Raj, Sheldon would allow to "mate" with his sister, there is the added "insurance" of getting any smart genes from any of the 3 Lothario's mentioned above.
If you are going to try to argue with a geneticist about genetics, please use the correct terms. Sheldon is not referring to a recessive gene - there is no such thing as a dormant gene - he is speaking of a randomly mutated gene. Those are the words he used. If he had inherited a homozygous recessive karotype - one recessive gene from each of his parents - then somewhere in his family tree there would similarly gifted people, in which case he would use the correct term - a recessive gene. If Missy is a heterozygotic dominant karotype possessing the recessive gene for super-genius and the dominant for ordinary intelligence then mating her with Howard, Raj or Leonard would be a waste of time as their dominant genius gene would prevent the recessive super-genius gene from being expressed in the phenotype of the resulting child. The child would be highly intelligent but not on Sheldon's standards. It doesn't matter if Sheldon does not know any of this as he refers several times to a randomly mutated gene, not a recessive one. Missy does not carry the super-genius gene. The posting is correct.
Sheldon is prone to magical thinking when necessary to preserve his obsessive need to control his environment. He may have simply ignored the flaw in his reasoning, as even the most intelligent humans do when venturing outside their ares of expertise. He may be interested in the science of genetics, but his Ph.D. in physics doesn't qualify him as an expert in that field.