Plot hole: In Series 1, Episode 7, "The Dumpling Paradox, " Sheldon makes an oblique reference to his financial status: "Frankly, if I could afford the rent, I'd ask you [Leonard] to leave, " meaning he cannot pay the rent on his two bedroom apartment by himself - not that he doesn't want to, he can't. However, in "The Execlsior Acquisition, " we find that he does not even cash his pay cheques. He doesn't even deposit them into a bank account - he leaves them in a drawer in his desk. In Series 2 Episode 14 "The Financial Permeability", he lends Penny a large amount of money from a huge bankroll he just happens to have lying about - again, without cashing his pay cheques! He is obviously independently wealthy. Either he doesn't have enough money to afford the rent or he has enough to work without being paid while practically giving large amounts of cash away. Can't be both.
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.
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