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.
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)
Other mistake: When Mary is rubbing VapoRub on Sheldon's chest, she makes a comment that last time she saw that there was no hair, to which Sheldon replies "Yeah it filled in last year." In Season 1, Episode 11, Penny rubs VapoRub on Sheldon's chest and a very clear remark about chest hair was made. Season 1 for the show was 4 years ago.Ashish_Agrawal
Continuity mistake: When Sheldon and Leonard are in the kitchen discussing Leonard's upcoming night out with Mrs. Latham, there's a plastic bottle of orange juice on the table that keeps disappearing and reappearing as the camera switches between Sheldon and Leonard.
Continuity mistake: In "The Luminous Fish Effect" (S1E04) Sheldon tells Penny he weighs 140 pounds. In "The Porkchop Indeterminacy" (S1E16), he tells his sister he weighs 165. 25lbs difference would be a noticeable change, but he looks the same.MFWills
Continuity mistake: Sheldon and Amy are talking while drinking tea together. The entire time, Sheldon has his hand next to his other hand, but in an individual shot, his hand is suddenly on his other wrist.bobthedancingdonut
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?
Factual error: The foam Sheldon used on Kripke consists of mixing ordinary dish soap, hydrogen peroxide, and saturated potassium iodide. That kind of exothermic reaction is dangerously flammable, so it should have severely burned Kripke and the members of the university board when it fell on them.
Continuity mistake: In the early episodes, Leonard is depressed and buys cat stuff. He comments that he has taken in to account Sheldon's asthma with a hyper allergenic cat. Later in the series it is Leonard with asthma and Sheldon who gets all the cats.
Continuity mistake: In the beginning of the series Sheldon knocks on Penny's door only once. Later in the series Sheldon explains he has always knocked 3 times because he walked in on his father with another woman.