Continuity mistake: When Penny is making French toast and Sheldon walks into shot, the edges of the toast are not covered in egg whilst the rest of the toast is. About 30 seconds later, Penny asks Sheldon if he wants French toast and the edges are still not covered in egg. The shot cuts to Sheldon. In this shot we can see Penny's hands to the far edge of screen and fully raised showing us that she hasn't dipped the edges of the toast in egg yet. But in the next shot, we can see the whole of the toast is covered in egg, including the edges of the toast that were clear a moment earlier. (00:00:20 - 00:00:50)
Character mistake: Sheldon refers to using the spray bottle as negative reinforcement when it is in fact positive punishment. Reinforcement involves encouraging a behaviour by either adding or removing a stimulus whereas punishment involves discouraging a behaviour by adding or removing a stimulus. Sheldon would know the difference.
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.
Character mistake: When Sheldon is placing his order near the beginning of the episode, he states "In the mid-18th century, King Rama IV of Siam..." King Rama IV was born 18th October 1804 and died 1st October 1868. His reign was during the mid-19th century (1851-1868).
Continuity mistake: Penny and Bernadette are working and Penny write her hair was in two braids with clips on top. But the second time we see her (same work shift), her hair is partially pulled back with bangs.
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: 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.
Continuity mistake: When Howard is proposing to Bernadette she is holding a tray with two glasses on it. The glasses are next to each other, side by side for two shots of her. Then in the third shot the glasses move so one is behind the other. Then in the fourth shot they are side by side again.
Factual error: The foam Sheldon used on Kripke consists of mixing ordinary dish soap, hydrogen peroxide, and saturated potassium iodide. That kind of exothermic reaction is dangerously flammable, so it should have severely burned Kripke and the members of the university board when it fell on them.
Character mistake: When working in the Cheesecake Factory, Sheldon says "Bonne appétite," with a hard T at the end. He should know that this is incorrect and would be the first to remind others that the correct phrase is "Bon appétit" (pronounced "appéti" - it is masculine and the t at the end is not pronounced).