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.
Continuity mistake: Sheldon puts the bag in the bin at the start of the episode so that the handles are facing the ground. When he gets the bag out, the handles are at the top of the bin.
Audio problem: When Sheldon is knocking on Leonard's door at the start, the sound is out of sync with the action.
Continuity mistake: When Penny is telling Howard and Raj about Sheldon's "drug addicted cousin" her scarf keeps jumping in and out of her jacket.
Continuity mistake: In nearly every episode, Sheldon demonstrates his OCD when he knocks three times on a door, says a person's name, and repeats that sequence twice, for a total of three iterations, but in this episode he radically departs from that behavior not once but twice. First, wanting to talk to Leonard, he knocks four times, says "Leonard" and repeats the sequence three times for a total of four iterations. Later, wanting to talk to Penny, he knocks four times and says her name, repeating that sequence at least four more times. Given that this was the first season, I assume the writers had not yet settled upon the 3x3 routine as a comic behavior.
Continuity mistake: During the whole opening scene, the way in which Leonard holds the letters in his hands keeps differing.
Continuity mistake: Sheldon puts the bag of takeout into the lobby trash can and as he does so, the whole bag turns sideways. At the end of the scene, he takes the bag out of the can and it's upright without him turning it.
The Pancake Batter Anomaly - S1-E11
Continuity mistake: After Leonard gives Penny her pile of mail, she alternates from holding the pile by her side to at her front between each shot. (00:01:10)
The Pancake Batter Anomaly - S1-E11
Continuity mistake: When Sheldon walks out his bedroom wrapped in a comforter, he drops it on the higher level before the drop down to the kitchen. In the next shot as he walks away from the fridge, half of the comforter is now spread over the lower level without anyone moving it. (00:05:10)
The Pancake Batter Anomaly - S1-E11
Continuity mistake: The way Penny holds her notepad when talking to Sheldon at the Cheesecake factory keeps changing instantly. (00:10:10)
The Pancake Batter Anomaly - S1-E11
Factual error: Leonard's myopia is greatly exaggerated in this episode. Even with high myopia he should still be able to navigate his apartment without aid especially after living there for seven years. (00:17:40)
The Jerusalem Duality - S1-E12
Visible crew/equipment: When Dr. Gablehouser is giving his speech about Dennis joining them, stage lights are reflected in his glasses and his wine glass. (00:16:30)
The Bat Jar Conjecture - S1-E13
Continuity mistake: When Raj is talking about psychological warfare he has a fork in his hand in one shot and not in the next. (00:08:40)
The Bat Jar Conjecture - S1-E13
Continuity mistake: At the end, when Leonard is gloating over beating Sheldon, his position on the sofa keeps changing in relation to the arm. (00:18:50)
The Nerdvana Annihilation - S1-E14
Continuity mistake: In the scene where Leonard is packing up his collectables to sell, at 15:32 he is dusting what appears to be a Hasbro Marvel Legends Yellow jacket figure, which also has a yellow post-it on the back. At 15:42 he is still dusting a figure but he now holds a different (darker but not yellow) figure from the same series, with no post-it on the back, and the Yellow jacket figure is now on the table (house left of the box of collectables). At 15:56 The Yellow jacket figure has disappeared from the table, and it is not the figure in Leonard's hands either. (00:15:30)
The Nerdvana Annihilation - S1-E14
Factual error: The time machine in this episode is supposedly the same one used in the H.G. Wells movie, but there are mistakes in the controls that would have been obvious to the characters: 1. When Leonard first gets into the machine he talks about traveling into the past and says something like "I'm setting the date to..." That is the method used to operate the Wayback Machine in the Rocky and Bullwinkle cartoon, but not the time machine in the H.G. Wells movie. Rod Taylor could not set the desired date on the controls, he simply used the lever to move forward and backward through time and the date display updated automatically to show the current date. 2. In the movie the default position of the lever was at a 45 degree angle. Pushing the lever forward moved the machine into the future, pulling back on the lever moved the machine into the past. In the TV show the default position of the lever is vertical and Leonard pulls the lever backwards to move forward into the future - opposite of the movie.
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 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.
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.
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.
The Pork Chop Indeterminacy - S1-E15
Continuity mistake: When Sheldon says that his sister was sent to spy on him, his arms are behind his back. Camera cuts and they are now at his side.