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.
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.
Other mistake: Sheldon would not have been able to crawl straight along the window ledge to Leonard's bedroom due to the layout of their apartment. Leonard's window is round a corner from Sheldon's.
The Einstein Approximation - S3-E14
Revealing mistake: In the scene where Sheldon visits Leonard and Penny in bed, towards the end of the scene, Leonard turns off the light. As he does, if you look carefully, you can see that the light turns off before he hits the switch.
The Einstein Approximation - S3-E14
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).
The Einstein Approximation - S3-E14
Continuity mistake: When Sheldon is looking for another job, the woman is holding a piece of yellow paper up. Camera cuts and she is no longer holding the piece of paper.
The Einstein Approximation - S3-E14
Character mistake: Sheldon is an extreme germophobe to the extent he doesn't even shake hands. There is no way he would be climbing around in a ball pit.
Suggested correction: If he was acting normally (for Sheldon), he wouldn't. However, Sheldon isn't acting as he normally would due to lack of sleep, and his obsession with solving a problem.
The severity of his phobia would not be minimized by lack of sleep.
Sheldon's mind is distracted by the problem he is trying to solve. He grabs other people's food, he allows Raj to touch his food, he handles dirty cutlery at the cheesecake factory, All characteristics that would be present if he was acting normally. The fact that he is in the ball pit is simply an extension.
Severe sleep deprivation could certainly affect how Sheldon reacts to phobias. The brain requires sleep to function and with a severe lack of sleep, the brain is no longer able to send the signals that alert Sheldon to his fear of germs.
The Einstein Approximation - S3-E14
Continuity mistake: When Sheldon is playing in the ball pit and Leonard is trying to coax him out the position of the black netting of the ball pit alternates between being and not being wrapped around the yellow entrance pillars.
The Large Hadron Collision - S3-E15
Continuity mistake: Penny asks Sheldon if the roommate agreement contains something about girlfriends, which Sheldon dismisses as unrealistic. However, it was revealed in season 2 that there is a cohabitation rider. This was revealed when Sheldon asserted that Leonard's girlfriend, Stephanie, was officially living with them.
The Large Hadron Collision - S3-E15
Factual error: At the very end of the show, Leonard and Raj arrive at the hotel, which is supposed to be in Geneva, Switzerland, to visit CERN. If you look out the "hotel" window, it looks like they're half way up Matterhorn, but in Geneva there are no big/rocky mountains anywhere near the city itself.
The Excelsior Acquisition - S3-E16
Plot hole: In Series 1, Episode 7, "The Dumpling Paradox, " Sheldon makes an oblique reference to his financial status: "Frankly, if I could afford the rent, I'd ask you [Leonard] to leave, " meaning he cannot pay the rent on his two bedroom apartment by himself - not that he doesn't want to, he can't. However, in "The Execlsior Acquisition, " we find that he does not even cash his pay cheques. He doesn't even deposit them into a bank account - he leaves them in a drawer in his desk. In Series 2 Episode 14 "The Financial Permeability", he lends Penny a large amount of money from a huge bankroll he just happens to have lying about - again, without cashing his pay cheques! He is obviously independently wealthy. Either he doesn't have enough money to afford the rent or he has enough to work without being paid while practically giving large amounts of cash away. Can't be both.
Suggested correction: Not being able to afford doesn't necessarily mean he doesn't have the money, especially a man like Sheldon. He works with a budget and he sticks to it. In his budget he has a certain amount set aside for rent, anything more than that and he can't afford it alone.
Nonsense. If he was sticking to a "rigid budget" he wouldn't have even thought of lending a hopeless credit risk like Penny a single cent. Instead he throws a huge bankroll at her without even discussing a repayment plan.
Rubbish, I stick to a strict budget but still have the money to lend to close friends. Like Penny is to him.
He might have different budgets for different things. People could get a higher margin because they could be of more use to the scientific mind of Sheldon.
The Excelsior Acquisition - S3-E16
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.
The Precious Fragmentation - S3-E17
Continuity mistake: At the cheesecake factory, the necklace is wrapped around his middle and ring fingers, then in the next shot, he is just holding it. (00:08:00)
The Precious Fragmentation - S3-E17
Continuity mistake: When eating at the Cheesecake Factory, the position of Raj's hamburger bun changes from shot to shot. (01:06:00 - 02:07:00)
The Precious Fragmentation - S3-E17
Continuity mistake: When Sheldon sneaks into Leonard's bedroom while Leonard and Penny are sleeping, Penny has her arms out over the blanket and Leonard has his on his pillow in front of his face. When Sheldon leans over Penny only her hands are on top of the covers and Leonard's are tucked under his pillow.
The Wheaton Recurrence - S3-E19
Factual error: Sheldon and the team are league bowling and have a match with Will Wheaton's team. They are bowling on lanes 2 and 3. In league bowling, you have to bowl on lanes that start with an odd number because the ball return is shared between those lanes. In league bowling, you take turns with each lane so that any differences in the lanes evens out, and this lane layout wouldn't allow that.