The Vengeance Formulation - S3-E9
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.
The Vengeance Formulation - S3-E9
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.
The Vengeance Formulation - S3-E9
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.
The Vengeance Formulation - S3-E9
Continuity mistake: When Leonerd sits on the whoopie cushion, he picks it up and it has creases in. Camera changes and the creases have changed.
The Vengeance Formulation - S3-E9
Character mistake: When Leonard, Sheldon, and Raj are watching Kripke entering his office with the board of directors, Kripke says "President Siebert", yet Siebert is not among the people standing with him.
Answer: Because Raj's selective mutism seems to be caused by women that Raj sees (on some sort of conscious or subconscious level) as a potential sexual partner. An attribute that wouldn't apply to either his sister or mother.