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 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
Continuity mistake: When Sheldon says the line about having no peers when cleaning the apartment, there is a pair of jeans on the side which disappears when the camera cuts. (00:10:00)
The Big Bran Hypothesis - S1-E2
Continuity mistake: When cleaning Penny's apartment, Sheldon is holding up a jacket. Camera cuts and he is no longer holding the jacket up. (00:09:50)
The Big Bran Hypothesis - S1-E2
Continuity mistake: When Leonard and Sheldon are pushing the box up the stairs, the position of the box on the stairs changes instantly. In one shot it is flush against the wall, then in the centre of the stairs. (00:05:20)
Other mistake: Leonard says that it's 2am when his door is knocked on, but when he opens his door to confront Sheldon, his window outside shows daytime light. (04:12:00 - 04:25:00)
The Big Bran Hypothesis - S1-E2
Other mistake: Leonard is awoken by the apartment door closing. When he walks into the living room the door is open. (00:08:55)
Suggested correction: He's awoken by a door closing, not necessarily the front door. He could have heard Sheldon closing his door.
The Big Bran Hypothesis - S1-E2
Continuity mistake: When shifting the box along the floor of the 3rd floor landing, Leonard's grips on the box is constantly changing. (00:06:00)
The Big Bran Hypothesis - S1-E2
Visible crew/equipment: At the very start, Raj walks over to his seat and a tape marker is visible on the floor. (00:00:05)
Visible crew/equipment: When Leonard, Sheldon and Penny are eating lunch for the first time, Penny sits on Sheldon's spot, Leonard then tells him to "Just sit somewhere else." He then walks over to his desk chair and contemplates sitting there and in the bottom left of the shot there is a chair with 4 false legs, and one large leg running down the middle. (00:08:20)
Continuity mistake: When Penny is talking to Leonard about who read her Ex's blog, she has a spoon full of ice-cream. Camera cuts and it's now empty. (00:05:00)
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 Grasshopper Experiment - S1-E8
Continuity mistake: When Raj starts talking to Penny after he drinks the Grasshopper drink in her apartment, in one frontal shot he lifts the drink and begins to drink but in the next shot from behind the drink is back on the counter.