Other mistake: Leonard says he had a growth spurt after his high school prom. In "The Cooper-Hofstadter Polarization" he told Penny that he still had all his clothes he owned since the eighth grade, after his last growth spurt.
The Clean Room Infiltration - S8-E11
Other mistake: When Howard, Leonard, and Raj are arguing in the clean room, Howard says that Leonard is jealous because Howard and Leonard used to be "best friends until Koothrapali came along." Yet, in the earlier seasons, we know that Howard and Raj already knew each other when Leonard met them for the first time and brought them back to the apartment to play video games. Meaning they couldn't have been best friends before Raj came along.
Suggested correction: Not being able to afford doesn't necessarily mean he doesn't have the money, especially a man like Sheldon. He works with a budget and he sticks to it. In his budget he has a certain amount set aside for rent, anything more than that and he can't afford it alone.
Nonsense. If he was sticking to a "rigid budget" he wouldn't have even thought of lending a hopeless credit risk like Penny a single cent. Instead he throws a huge bankroll at her without even discussing a repayment plan.
Rubbish, I stick to a strict budget but still have the money to lend to close friends. Like Penny is to him.
He might have different budgets for different things. People could get a higher margin because they could be of more use to the scientific mind of Sheldon.