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 Discovery Dissipation - S7-E10
Continuity mistake: In Season 3 Episode 1 Sheldon made a retraction of his paper. But here he says he had only one retraction, when he was a kid. (00:11:36 - 00:13:09)
Continuity mistake: Raj talks in front of Penny near the beginning of the episode, then picks up dishes, walks toward the kitchen, and just disappears from the set.
Suggested correction: Couple of points here, 1. Raj talking in front of Penny is already listed. 2. Raj doesn't pick the plates up until Penny has left after the Halo game. 3. He then stays in the kitchen area while we see Penny come back and settle down to go to sleep and Leonard and Sheldon go to bed and turn the lights out. Raj then creeps out the apartment and scares Penny.
The Higgs Boson Observation - S6-E3
Other mistake: Just before Amy video chats Sheldon there is a shot where she is wearing glasses, and when the camera zooms out she isn't.
The Grasshopper Experiment - S1-E8
Deliberate mistake: At the end, Penny holds up a bottle of rum to show Leonard that she added it to his drink. However, the B is missing from the name "Bacardi" (00:19:30)
The Hamburger Postulate - S1-E5
Visible crew/equipment: At the start when we see the guys sat at the table, a small white tape marker is visible on the floor where Penny will stand in a few minutes. (00:02:30)
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 Dead Hooker Juxtaposition - S2-E19
Continuity mistake: After the guys leave and Penny and Sheldon are eating alone, Sheldon's chopsticks switch between an unevenly broken pair of chopsticks and an evenly broken pair of chopsticks.
The Big Bran Hypothesis - S1-E2
Continuity mistake: When Sheldon is cleaning, he moves an iPod dock and the iPod lights up. Camera changes and the iPod is unlit. A few shots later it's lit again. (00:09:00)
The Big Bran Hypothesis - S1-E2
Visible crew/equipment: When Leonard opens the door at the start a yellow tape marker is visible in the centre of the door way. (00:00:40)
The Hamburger Postulate - S1-E5
Revealing mistake: When Penny leaves when Leonard and Leslie are in his room, she opens the apartment door and the hallway is isn't present. It's just a chipboard wall. (00:09:50)
The Proposal Proposal - S11-E1
Continuity mistake: When Penny and Bernadette are talking in the kitchen, the string for the teabag in Bernadette's yellow mug keeps moving between shots.
The Panty PiƱata Polarization - S2-E7
Continuity mistake: When Leonard talks to Penny about having to live with Sheldon he has his hand up to his chest. Camera swaps to a side view and his hand is not in front of his chest any more. (00:07:30)
The Griffin Equivalency - S2-E4
Continuity mistake: When Raj asks the guys who's going to the party on Saturday night, Penny's grip on the martini glass she has changes between shots. (00:10:20)