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)
The Barbarian Sublimation - S2-E3
Continuity mistake: When Penny explains she has bought the game, her grip on the laptop changes. (00:06:50)
The Barbarian Sublimation - S2-E3
Continuity mistake: At the start, after Penny has dropped one bag, there is an item in the top of the remaining bag. This item keeps appearing and disappearing. (00:01:20)
Continuity mistake: When Leslie and Leonard are talking about starting a relationship again, the can of Diet Cola keeps rotating. In some shots from Leslie's point of view you can't see the logo and in others you can. (00:06:30)
Continuity mistake: When Leonard says he is happy Penny is moving on he has nothing in his hand. Camera cuts and now he is holding a bit of bread. (00:03:00)