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 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 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 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 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 Spaghetti Catalyst - S3-E20
Continuity mistake: When Raj and Leonard are sitting on the couch, Leonard is holding Watchmen and Lost in Space in his left hand and Young Sherlock Holmes in his right. In the very next shot when Leonard turns his head after Raj speaks, Watchmen has disappeared.
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 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 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 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.