The Dependence Transcendence - S10-E3
Continuity mistake: Bernadette is talking to Raj's dad on the video phone. In the close up, her fingers are wrapped round the phone but in the long shot, she is holding her fingers behind it and balancing it with her thumb.
The Financial Permeability - S2-E14
Continuity mistake: Sheldon opens the can with money in and puts the lid on the side, However in some shots he has the lid in his hand. (00:04:00)

The Financial Permeability - S2-E14
Continuity mistake: When Sheldon is holding the money out to Penny, the can that is being held by Sheldon is constantly moving up and down in height in relation to his shirt. (00:04:00)

The Killer Robot Instability - S2-E12
Continuity mistake: When Penny and Howard are arguing near the start, Penny has her arms crossed in one shot and down by her side in the next. (00:04:50)

The Panty PiƱata Polarization - S2-E7
Continuity mistake: At the start when Howard is asking about the house, the pencil in front of him keeps moving on the table. Note the point and the edge of the table. (00:02:30)
The Cooper-Nowitzki Theorem - S2-E6
Continuity mistake: When Ramona starts talking to Sheldon in the cafeteria, the way Sheldon holds his knife and fork changes between shots. (00:04:00)
The Cooper-Nowitzki Theorem - S2-E6
Continuity mistake: The way Ramona holds her drink in the cafeteria changes between shots. (00:03:50)

The Cooper-Nowitzki Theorem - S2-E6
Continuity mistake: At the start as Leonard says about being able to talk to women, he puts his hand on his drink. Camera cuts and now his hand is back by the edge of the table. (00:02:50)

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)
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)
Suggested correction: Not being able to afford doesn't necessarily mean he doesn't have the money, especially a man like Sheldon. He works with a budget and he sticks to it. In his budget he has a certain amount set aside for rent, anything more than that and he can't afford it alone.
Nonsense. If he was sticking to a "rigid budget" he wouldn't have even thought of lending a hopeless credit risk like Penny a single cent. Instead he throws a huge bankroll at her without even discussing a repayment plan.
Rubbish, I stick to a strict budget but still have the money to lend to close friends. Like Penny is to him.
He might have different budgets for different things. People could get a higher margin because they could be of more use to the scientific mind of Sheldon.