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.
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 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 Plimpton Stimulation - S3-E21
Continuity mistake: When Sheldon, Penny, and Leonard are discussing Leonard's tryst with Dr. Plimpton, Penny pinches the bridge of her nose with her right hand. The shot changes and Penny brings her left hand down from her face.
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 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 Electric Can Opener Fluctuation - S3-E1
Continuity mistake: Sheldon's Sandwich goes from looking burnt to not burnt in the next few frames. (00:16:56)
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 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 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 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 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.