Factual error: Sheldon says the movie Gremlins "baffles" him in regards to the instructions being very clear."Don't feed the gremlins after midnight." However, this instruction is only for caring of a Mogwai, not gremlins (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 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 part of the way back in the first place was to check just that.
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).
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.
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: Sheldon's voice becomes squeaky when helium is pumped into his office. But if the room contained enough helium to make his voice squeaky just by breathing, Sheldon would actually be suffocating due to lack of oxygen, the lighter helium having displaced the heavier oxygen. You can do it with a balloon because you can breathe normal air between huffs, but if you're in a room full of helium, you won't last long before passing out and asphyxiating.
Character mistake: The proposition that danishes wouldn't exist if Copenhagen were flooded is wrong, because "danishes" were created by Austrian bakers. They are called danish in English-speaking countries because they're very popular in Denmark. The Danish word for this pastry is wienerbrød, which translates to "Viennese bread."
Factual error: Raj and Sheldon are watching TV in Raj's apartment and we hear music playing. Sheldon asks if the woman on TV was Aishwarya Rai to which Raj says yes and then they argue about her and Madhuri Dixit. The song playing was from the Bollywood movie Kaho Na Pyar Hai, but neither of them are in the movie - the lead actress was Ameesha Patel.
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: In his argument with Leonard regarding Superman's ability to fly, Sheldon states that in Superman 1, Lois Lane is two feet off the ground when Superman catches her as she falls from the helicopter. Not so. Superman catches Lois at least ten stories up. Additionally, both Penny and Sheldon say Superman "swoops down" to save Lois. Penny can be forgiven, but Sheldon would know better: Superman flies UP from ground level to catch Lois.
Continuity mistake: When Howard is almost done moving out of his mother's house, there is a table in front of him with a measuring device in the top corner. In one shot, the device moves to the opposite corner of the table. In a few shots later, the item returns to its original position.
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.
Continuity mistake: When Howard is on the mound, the shot from behind the plate shows a player ready to catch the ball in a uniform shirt. The next long shot from the stands shows a catcher in full gear, and then back to behind the plate to the player in uniform shirt only.
Character mistake: When Howard says they should put the time machine into the elevator in 1-14 "The Nerdvana Annihilation", Leonard states the elevator had been broken for two years, but in this episode, we found out the elevator broke seven years earlier.
Character mistake: When Sheldon arrives at the apartment with his Nintendo 64 in the box, he tells Leonard that they can play Super Mario 64. He then proceeds to say, upon finding a memory card, that they can pick up where he left off. Super Mario 64 does not make use of the memory card for progression, all of that data was saved on the cartridge.
Revealing mistake: In the scene where Leonard is supposedly playing Halo 3 against somebody in Copenhagen, there is no ethernet cable or wireless adapter connected to the Xbox 360 (one of the originals without wireless inbuilt), which means that there is no way he can be playing online with someone in another country.