Continuity mistake: When Leonard is consoling Penny on the couch, the blue Afghan she has with her constantly changes position, including jumping from the floor back to the couch.
The Hamburger Postulate - S1-E5
Continuity mistake: When Sheldon is explaining to Leonard why a Cheesecake Factory Hamburger is superior to a Big Boy Hamburger the number of fries on Leonard's plate noticeably changes between shots.
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 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 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 Bat Jar Conjecture - S1-E13
Continuity mistake: When Raj is talking about psychological warfare he has a fork in his hand in one shot and not in the next. (00:08:40)
The Hamburger Postulate - S1-E5
Continuity mistake: When Sheldon is ranting about his board being changed, there is one shot where his hand is uncovered then covered by the blanket. (00:12:00)
The Hamburger Postulate - S1-E5
Continuity mistake: When Howard demonstrates being a human beat box to Penny, the way she holds her pen changes instantly. (00:02:50)
The Luminous Fish Effect - S1-E4
Continuity mistake: When Penny is asking if Sheldon has ever done anything like this before she is holding her plate with 2 hands in one shot and 1 hand in the next. (00:13:20)
The Luminous Fish Effect - S1-E4
Continuity mistake: When Sheldon asks his mum why she's there, his mums hand on his chest changes position. Note the distance to his elbow. (00:11:40)
The Luminous Fish Effect - S1-E4
Continuity mistake: At the buffet, Sheldon has 2 hands on his plate. Camera cuts and now he has one hand by his side. This is before Howard walks in with his date. And the cut is instant. (00:02:00)