Continuity mistake: In the laundry room when Penny is talking to Sheldon, Sheldon takes some time arranging a blue shirt on his plastic laundry folder. Then it suddenly turns into a pair of socks, which he folds and then picks up the blue shirt again. There was not enough time for him to switch out the shirt for the socks.
New this week Continuity mistake: The Stevenson Award in Sheldon's office reads "Sheldon Cooper, PhD." But, in the "Dennis Kim" episode we are told Sheldon was 14.5 years old when he earned that award - 1.5 years before earning his PhD at age 16, so the award should not show the title of PhD.
New this month Continuity mistake: When Sheldon sneaks into Leonard's bedroom while Leonard and Penny are sleeping, Penny has her arms out over the blanket and Leonard has his on his pillow in front of his face. When Sheldon leans over Penny only her hands are on top of the covers and Leonard's are tucked under his pillow.
New this month Continuity mistake: When Leonard is standing outside the apartment his hair is tucked under the band of the wireless cam he has on his head, but when he is crawling on his hands and knees through the apartment his hair is out from under the band and is hanging in front of his face.
Factual error: At the very beginning of the episode Leonard says "So you see what you're eating is not technically yogurt because it doesn't have enough live active acidophilus cultures." He is implying this is a scientific fact (he's not just giving his opinion on yogurt.) But to meet the U.S. standards for yogurt, only the starter cultures Lactobacillus bulgaricus and Streptococcus thermophilus are required, not Lactobacillus acidophilus. The presence or absence of L. acidophilus does NOT determine a food's identity as yogurt (which Leonard's line is implying).
Factual error: There is not a snowball's chance of Howard becoming an astronaut. He suffers from Intermittent Cardiac Arrhythmia, something about which he is completely open. 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.
Factual error: Penny picks up a hand gun, pulls back the slide to ensure the chamber is empty and 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. Problem is, Penny would have had to work the slide again to get a bullet from the magazine into the chamber for this to happen. She pulled the slide far enough back that if there had been a bullet in the chamber already it would have ejected.
Continuity mistake: At the end when Sheldon has got a burger, the amount of burger left changes depending on the camera angle. Most noticeable when he asks Penny about permanently reserving the table - between shots the lettuce disappears, the bun changes colour, and the bite marks change.
Character mistake: Being the first to play in the "time machine," Leonard says he will set the date for March 10,1876. Howard says "Good choice. Alexander Graham Bell invents the telephone and calls out for Doctor Watson." Bell's assistant, Thomas A. Watson, was an experienced electrical designer and mechanic, but he did not hold an advanced degree. It is well documented that the first words transmitted over the telephone identified him as Mister Watson.
Character mistake: When working in the Cheesecake Factory, Sheldon says "Bonne appétite". He should know that this is incorrect and would be the first to remind others that the correct phrase is "Bon appétit" (appétit is masculine and the t at the end of the word is not pronounced). He may be confusing the phrase with the German "Guten appetit" or the Italian "Buon appetito", but this is unlikely as using the French "Bon appeéit" is the standard English phrase. Minor character mistake for most people, but not Sheldon.
Factual error: During the final scene of this episode, Sheldon steps out of his office wearing a gas mask and engages Leonard in conversation where he then states he is making hydrogen sulphide gas (more commonly known as H2S). Leonard correctly identifies this as highly flammable. However, this gas is far more dangerous and is harmful to the human body at as low a concentration as 20 parts per million (ppm), can cause permanent damage at 100ppm and is fatal after two breaths at 500ppm. So for Raj (and his bird) to be completely unharmed in a high concentration of H2S (noted by the fire) is impossible.