Continuity mistake: In the scene where Leonard is packing up his collectables to sell, at 15:32 he is dusting what appears to be a Hasbro Marvel Legends Yellow jacket figure, which also has a yellow post-it on the back. At 15:42 he is still dusting a figure but he now holds a different (darker but not yellow) figure from the same series, with no post-it on the back, and the Yellow jacket figure is now on the table (house left of the box of collectables). At 15:56 The Yellow jacket figure has disappeared from the table, and it is not the figure in Leonard's hands either.
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: 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: Sheldon says the movie Gremlins "baffles" him in regards to the instructions being very clear."Don't feed the gremlins after midnight. Don't get the gremlins wet." However, these instructions are only for caring of a Mogwai, not gremlins (and the gremlins are formed by Mogwais eating after midnight). Sheldon, of all characters, would not mistake Mogwais for Gremlins and he would know the exact wording of the instructions.
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.
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.
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.
Factual error: The "Hollermus" that Sheldon allegedly makes is not actually a Swiss breakfast dish. It is in fact simply a kind of jam made from elderberries which is quite common in most German-speaking countries. Also, judging by the ingredients on the table (eggs, milk, butter) and the food on the plate, the dish prepared by Sheldon seems most likely to be an omelette with a Vienna sausage, which is in no way traditionally Swiss.
Factual error: Leslie Winkle takes shelter with Howard in the middle of a paintball game. Her gun has no hopper for paintballs and thus no ammo, so it's useless, despite her apparently using it outside seconds earlier. This isn't a model with an internal magazine - the port to attach the missing hopper is plainly visible.
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.
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.