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.
The Flaming Spittoon Acquisition - S5-E10
Factual error: Sheldon and Amy have agreed to call each other "boyfriend" and "girlfriend." Sheldon suggests she should peruse the new relationship agreement while he sets up his notary stamp. As an agreement, both parties would sign. As a Notary, Sheldon would know that he could not notarize his own signature.
The Beta Test Initiation - S5-E14
Factual error: Penny picks up a hand gun, pulls back the slide to ensure the chamber is empty (which would discharge any round in the chamber too) and then releases it, leaving it closed. She then loads a magazine into the butt of the weapon and hands it to Leonard. He starts to smooch her and shoots himself in the foot. The gun could not have fired, because Penny would have to pull the slide all the way back and then release it again to load the first bullet. There couldn't have already been a bullet in the chamber, as the whole reason Penny pulled the slide back in the first place was to check just that.
The Recombination Hypothesis - S5-E13
Factual error: Leonard lies to Sheldon about his being over at Penny's at 3am by saying he went across the street to use the gas station bathroom. Sheldon refers to it as "The Colorado Boulevard Chevron." The address of their apartment building is 2311 N. Los Robles. Colorado Boulevard is five miles away. (Yes, it's a fantasy sequence, but even in Leonard's head, Sheldon's not likely to make a mistake like that). (00:15:45)
The Ornithophobia Diffusion - S5-E9
Factual error: Sheldon is fearful of the bird on his windowsill, which he identifies as a blue jay. Blue Jays are not native to CA. The bird is actually a scrub jay. Sheldon would know this because of his lifetime fear of birds.
The Isolation Permutation - S5-E8
Factual error: Amy is sitting outside a liquor store that shows a sign indicating it is open 24 hours. However, that's a crime in CA. Any on-sale or off sale licensee, or agent or employee of that licensee, who sells, gives, or delivers to any persons any alcoholic beverage or any person who knowingly purchases any alcoholic beverage between the hours of 2 o'clock a.m. and 6 o'clock a.m. of the same day, is guilty of a misdemeanor.
The Launch Acceleration - S5-E23
Factual error: In all the episodes leading up to Howard and Bernadette's wedding, Howard was going into space to install a space toilet. But in this episode, Howard tells her they want his telescope, so he has to go.
Suggested correction: The space toilet was something Howard designed that NASA installed back in season 2. His mission to the ISS in season 5 was always about his telescope. In episode 5, "The Russian Rocket Reaction", Howard says NASA picked his team's design for the deep field space telescope that's going on the International Space Station in the spring.