Deliberate mistake: Very often, during Skype or other video chat conversations, the people on the computer screen look left or right when talking to someone who is not directly in front of the screen. Although it certainly helps the viewers understand who's talking to whom (which is why I assume it's a 'deliberate mistake'), it isn't realistic, since it implies that the people on the screen are actually constantly looking away from their computer instead of at their screen or webcam.
Deliberate mistake: Whenever anyone walks across the front hallway, it takes them 6-7 seconds to walk from one stairway to the other. On the backside of the stairway, it only takes 1-2 seconds to walk across.
The Grasshopper Experiment - S1-E8
Deliberate mistake: At the end, Penny holds up a bottle of rum to show Leonard that she added it to his drink. However, the B is missing from the name "Bacardi" (00:19:30)
The Retraction Reaction - S11-E2
Deliberate mistake: Leonard is on NPR on a Friday, and the guys don't talk about it until the following Monday at work. They spend so much time together, they surely would've discussed it sooner.
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.