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.
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Character mistake: When Howard says they should put the time machine into the elevator in 1-14 "The Nerdvana Annihilation", Leonard states the elevator had been broken for two years, but in this episode, we found out the elevator broke seven years earlier.
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.
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).
Character mistake: When working in the Cheesecake Factory, Sheldon says "Bonne appétite," with a hard T at the end. He should know that this is incorrect and would be the first to remind others that the correct phrase is "Bon appétit" (pronounced "appéti" - it is masculine and the t at the end is not pronounced).