The Big Bran Hypothesis - S1-E2
Visible crew/equipment: When Penny is having a go at Sheldon and Leonard, there is a shot of some metal pans with stage lights visible in them. (00:12:30)
The Big Bran Hypothesis - S1-E2
Audio problem: When Penny is talking to Raj on the stairs to the apartments, during some shots we see her from behind. In one shot, we hear her say something like "And I'm freaking out", but you can tell by the way her jaw moves that she was actually saying something different. (00:14:50)
The Big Bran Hypothesis - S1-E2
Continuity mistake: At the end of the episode, when the gang is reading the furniture assembly instructions, a pencil in the cup in front of them suddenly vanishes. (00:19:00)
The Big Bran Hypothesis - S1-E2
Continuity mistake: At the very end of the episode we see Penny with her hands on the corner of the piece of wood. Camera cut and now they are in the middle. (00:19:50)
The Big Bran Hypothesis - S1-E2
Character mistake: Sheldon does not do his 3x OCD knock on Penny's door.
Suggested correction: That quirk wasn't brought into the series until halfway through the first season. The one-knock Sheldon happened a couple of times before it became the three knock habit.
The Fuzzy Boots Corollary - S1-E3
Revealing mistake: When everybody is on their laptops at the beginning of the episode, you can clearly see in many shots that their screens are black. (00:01:20)
The Fuzzy Boots Corollary - S1-E3
Continuity mistake: When Howard sits down on the sofa saying about sexual harassment laws, his hand moves from his mouth to the side of his head instantly. (00:04:50)
The Fuzzy Boots Corollary - S1-E3
Continuity mistake: When Sheldon, Howard and Raj play Jenga, there is one block sitting at the top of the tower. When Leonard walks in, there are now two blocks at the top, before we actually see Howard place the second one on the top. (00:08:10)
The Fuzzy Boots Corollary - S1-E3
Continuity mistake: When Sheldon is telling Leonard that he didn't ask Penny out, there is a yellow food-bag on the counter between them that keeps changing its position with every shot change. (00:11:15)
The Luminous Fish Effect - S1-E4
Continuity mistake: When Leonard and Sheldon are walking downstairs, Sheldon stops and pins back up the caution tape that is in front of the elevator. Between shots, the other strip of caution tape untwists itself. (00:01:25)
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)
The Luminous Fish Effect - S1-E4
Continuity mistake: When Penny comes into the apartment to ask if Sheldon needs anything from the market, between the few shots, the position of the napkin and the pile of eggs on the plate he is holding changes. (00:05:15)
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: 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's mom is saying the prayer, the bread roll that Raj is holding swaps hands, and then it disappears in the shot where she tells them they don't have to join in with the end of the prayer.
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 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 Hamburger Postulate - S1-E5
Character mistake: Leslie states that heroin causes pupils to dilate, like when Leonard sees Penny. Opiates cause pupils to constrict. (00:06:20)
The Hamburger Postulate - S1-E5
Character mistake: When Sheldon knocks on Penny's door to seek advice about the tie on Leonard's doorknob, he does not use his typical triple knock. (00:07:43)
First time he knocks 3 times is in Episode 2 of Season 1. First time knocking 3 times followed by saying the name is episode 10 of Season 1. The ritual of 3 knocks and 3 times saying the name and then stopping is Episode 5 of season 2.
Sheldon knocks three times because he once walked into his parents bedroom and saw his father with another woman. He's been doing the triple knock since he was a teenager.
Yet, he didn't in the show till Season 2. Funny ain't it?
Suggested correction: A one-time lapse in someone's usual behavior does not count as a "character mistake", even in the case of someone given to ritualistic behavior as Sheldon is.
Ah, but in an episode he explains he had developed this particular ritual at age 13 after walking into his parent's bedroom without knocking and seeing his father having sex with another woman. He says he started knocking 3 times since then and would never forget. So its not consistent and a mistake as this is not the only example one can name.
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)