The Hofstadter Isotope - S2-E20
Continuity mistake: Near the end of a conversation with Stewart, Penny is holding a drawing that Stewart drew for her. In the next shot, it is now on the counter and she is picking it up.
The Vegas Renormalization - S2-E21
Continuity mistake: When Leonard and Raj are getting ready in the bathroom, Raj picks up a tube of shampoo/conditioner off the bathroom bench with his left hand. However, in the next shot, Raj has nothing in his left hand and the tube is back on the bench, with no time for him to replace it between shots.
The Vegas Renormalization - S2-E21
Continuity mistake: In the bathroom of the hotel in Las Vegas, we can see Rajesh taking a small white bottle and keeping it in his hand while saying "I love Las Vegas". In the next shot, the bottle has returned to its place instantly.
The Classified Materials Turbulence - S2-E22
Continuity mistake: In the comic book store, when Stuart and Leonard are talking about Penny saying "Leonard" when with Stuart, Stuart's pen/hand is constantly changing position instantly.
The Classified Materials Turbulence - S2-E22
Continuity mistake: When Raj is going through the ideas on what would work to fix the toilet, Sheldon's hand is not near his face, but when Howard talks about moving to Israel, Sheldon's hand is up by his face.
The Classified Materials Turbulence - S2-E22
Continuity mistake: Leonard is talking to Stuart at the door to his (Leonard's) apartment. Howard then comes over and slams the door in Stuart's face and Leonard has moved back about 4-ft instantly.
The Monopolar Expedition - S2-E23
Continuity mistake: When Penny finds out about the expedition, Sheldon starts to walk to his apartment. Camera cuts to Leonard in the apartment for five seconds and then to Penny in the doorway. Behind her, you can see Sheldon walking to the apartment still. Since he was halfway to start with, he should be in the apartment by now. (00:10:35)
The Gothowitz Deviation - S3-E3
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)
The Gothowitz Deviation - S3-E3
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.
The Creepy Candy Coating Corollary - S3-E5
Continuity mistake: At the dinner, Howard's mom calls. Howard's wine glass refills itself between shots. (00:15:20)
The Creepy Candy Coating Corollary - S3-E5
Other mistake: When Sheldon signs the entry sheet Stuart claims he wrote "Die Will Wheaton Die." But he was only writing for half a second to a second, he could never have written all that in the time frame.
The Creepy Candy Coating Corollary - S3-E5
Continuity mistake: Bernadette speaks regular here. In future episodes she suddenly has a higher-pitched voice.
Suggested correction: This isn't really so much a mistake as it was a character tweaking, which happens often in TV series.
The Adhesive Duck Deficiency - S3-E8
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).
The Adhesive Duck Deficiency - S3-E8
Factual error: Maybe I'm wrong but I've had the dislocated shoulder experience and shouldn't hers be in a sling at her side not across her front right to left? This just seems odd.
Suggested correction: That type of sling is the best for preventing movement of the shoulder joint. It is the proper one.
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 Maternal Congruence - S3-E11
Visible crew/equipment: When the four (Leonard, Penny, Sheldon and Beverly) are driving to the airport at the end, the studio lights are reflected in Beverly's sunglasses.