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.
Other mistake: While the group are trying to figure out how to play Halo without Howard, Leonard jokingly suggests cutting Raj in half. Raj responds, "Oh sure, cut the foreigner in half. There's a billion more where he came from." But Penny is in the room with them, so there's no way he should be able to talk in front of her, or even if he's been drinking, the fact alcohol helps him isn't realised until the next episode, so the fact he can speak with her there should have surprised everyone, including him.
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: 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: 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: 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.
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.
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.
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.