The Big Bang Theory
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The Thespian Catalyst - S4-E14

Revealing mistake: When Sheldon goes to Penny's apartment and they do a scene study together, they both read lines from a multi-page script that Sheldon brings with him. On a couple of occasions the camera cuts to a side view of Sheldon and we get to see the page of the script that he's currently reading from. The pages are completely blank.

The Herb Garden Germination - S4-E20

Revealing mistake: Sheldon's laptop has gone through several strange transformations throughout the series, but in this episode it takes the biscuit - it appears to be a Dell XPS with the back covered up, but the shot of Sheldon chatting only to Amy shows a Mac keyboard, with the laptop running OS X.

Moose

The Countdown Reflection - S5-E24

Factual error: There is not a snowball's chance of Howard becoming an astronaut. He suffers from cardiac arrhythmia, something about which he is completely open. "Transient" or not this is easily detectable by a simple electrocardiogram, which is a fundamental part of the many medical examinations a potential astronaut will have to pass. He wouldn't even be allowed to start basic training. Note also that during his basic training he shows signs of severe stress and trauma which would inevitably trigger a cardiac episode. Even if it didn't the fact that he was falling apart at the seams would have him removed from the programme for his own good.

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Trivia: During Season 3, the producers learned of a show called "The Theorists" in the country of Belarus that was a copy of this show. A lawsuit for copyright infringement would have been pointless since the production company for "The Theorists" was owned by the Belarus government. A lawsuit, however, was not needed because when the actors and actresses found out the show was a rip-off this one, they promptly quit and "The Theorists" was cancelled.

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The Euclid Alternative - S2-E5

Question: Though it comes up in other episodes as well, this one is focused on Sheldon needing a ride everywhere he goes because he can't drive, not to mention his not being welcome on the bus. Of course, this story element would be nonexistent if there was a simple answer, but it does beg the question: Does Pasadena not have taxicabs?

MFWills

Chosen answer: It does. The variable cleanliness of the cab and the habit of taxi drivers to engage customers in small talk would be too much for Sheldon to handle, and not an option for him.

Captain Defenestrator

Answer: Sheldon DID finally use a taxi when going to the airport to see and propose to Amy in New Jersey.

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