Character mistake: When Howard finds the stack of paychecks in Sheldon's drawer and wonders why Sheldon hasn't cashed them, Sheldon explains that he's saving them to purchase items that have yet to be invented and he doesn't trust banks. But just keeping them in his drawer doesn't do anything, because checks are voided after a set period of time and they would eventually become worthless.
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.
Factual error: In order to get vengeance on Kripke, Sheldon mixes a solution of hydrogen peroxide, saturated potassium iodide and liquid soap, creating a large foam blob. This is easy to replicate, and what you will get (and look carefully, it is what Sheldon gets) is a huge, aerated foam mass consisting almost completely of bubbles. It is barely heavier than air, and if dropped from a ceiling as we see later in the episode it would float harmlessly about the place. Whatever it is that drops on Kripke and his visitors later, it isn't the foam mixture we see earlier - it looks like some sort of custard mix.
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. (00:07:25)
Continuity mistake: After the 'Ramona' conversation between Sheldon and Penny ends, Sheldon leaves Penny alone on the couch. Penny looks up to the "Amy and Penny" painting and says "Don't look at me like that, I tried." In S10 E10, Amy gave the painting back to Penny, which was hung in Leonard's living room.
Revealing mistake: When Sheldon goes to Penny's apartment and they do a scene study together, they both read lines from a multi-page script that Sheldon brings with him. On a couple of occasions the camera cuts to a side view of Sheldon and we get to see the page of the script that he's currently reading from. The pages are completely blank.
Character mistake: When Howard is asking Sheldon engineering questions, the first question is "How do you quantify the strength of materials?" Sheldon answers "Young's Modulus," and Howard admits that is correct. But it's not correct - Young's Modulus quantifies a material's elasticity, not strength. (00:17:10)
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. (00:06:30)