A Solar Calculator, a Game Ball, and a Cheerleader's Bosom - S1-E5
Continuity mistake: When Connie is playing the slot machine at the end, the wheels land in a set order. She then has a chat with someone and then goes to spin again, but the wheels are in different positions than before. We see Connie through all of this, and she doesn't spin between the two instances outlined here. (00:17:30)
A Therapist, a Comic Book, and a Breakfast Sausage - S1-E4
Continuity mistake: When George Sr. is first trying to help Sheldon, who is choking, he has his left arm under Sheldon's body. When the shot changes, his left arm is across the back of Sheldon's neck. (00:00:40)
A Therapist, a Comic Book, and a Breakfast Sausage - S1-E4
Continuity mistake: When Connie is talking about her date possibly wanting some more of her, George Jr. has a fork in his hands. When the shot changes, his hand is at his mouth without a fork in it. (00:04:55)
A Therapist, a Comic Book, and a Breakfast Sausage - S1-E4
Continuity mistake: When Connie, George Jr., and Missy are sat in the car, eating ice cream, Missy goes from holding the spoon to not holding it and back to holding it, depending on the camera angle. (00:14:40)
A Therapist, a Comic Book, and a Breakfast Sausage - S1-E4
Continuity mistake: When Sheldon points out how big the sausage was that he choked on, he holds his hands up in the air to symbolize this. From the shot behind Sheldon, his hand is not visible. (00:03:00)
A Therapist, a Comic Book, and a Breakfast Sausage - S1-E4
Continuity mistake: When Tam moves his stuff on the lunch table, his arms are around his lunch. When the camera does an instant cut, his arm is no longer around his lunch. (00:03:30)
A Solar Calculator, a Game Ball, and a Cheerleader's Bosom - S1-E5
Continuity mistake: When George Sr sits down to talk statistics with Sheldon at the kitchen table, his beer bottle keeps rotating in his hand. Note the label. (00:08:30)
Continuity mistake: At the start, the cards in Sheldon's hands keep changing between shots. (00:00:40)
Rockets, Communists, and the Dewey Decimal System - S1-E2
Continuity mistake: When Tam mentions the Ku Klux Klan, Mary has nothing on her fork. When the shot changes, she's suddenly got some food on her fork. (00:15:40)
Little Green Men and a Fella's Marriage Proposal - S6-E18
Character mistake: When Dr. Bell examines baby Constance, she has the stethoscope in her ears facing backwards. Also, when Sheldon and the professors are looking at the data from the telescope, Dr. Linkletter says "what about that" and Dr. Prakash says "no, that's within the standard deviation." That doesn't make sense.
Suggested correction: Not taking anything away from the other correction, but these are two separate mistakes put into one entry.
Additionally, a "standard deviation" is a significant concept that helps scientists determine when they have actual results worth investigating.
A Stolen Truck and Going on the Lam - S6-E16
Character mistake: Missy and Paige are stopped by a police officer "just outside Baton Rouge" But in Texas, the family is told they are outside Boca Raton.
A Broom Closet and Satan's Monopoly Board - S3-E2
Continuity mistake: George invites Mary out to dinner on Friday. But while they are at dinner, Sheldon is attending his college class (with Dr. Linkletter) - which meets on Thursday.
Jiu-Jitsu, Bubble Wrap, and Yoo-Hoo - S1-E17
Continuity mistake: When Mary arrives at the bowling alley and is talking to Brenda, Brenda's hands are constantly changing between instant cuts. In some shots she's holding shoe freshener and in others it's shoes. (00:13:15)
German for Beginners and a Crazy Old Man with a Bat - S6-E20
Character mistake: Sheldon says that "entrez vous" is German for "come in." That is actually French.
Suggested correction: He says "eintreten."
Ants on a Log and a Cheating Winker - S7-E4
Other mistake: Sheldon (in the voice-over) says "it really brought what's his name and I closer together." The grammatically correct expression is "brought what's his name and ME closer together", and a stickler like Sheldon would not make that mistake.
A Sneeze, Detention, and Sissy Spacek - S1-E13
Continuity mistake: When the principal gets the paddle out of the drawer, he holds it in two hands. But as he goes to sit down, he is only holding it in one hand. (00:02:30)
Gluons, Guacamole, and the Color Purple - S1-E19
Continuity mistake: When Sheldon startles Connie in bed, Connie has her hands up by her head. Shot changes and her hand is now across her chest. (00:15:20)
Continuity mistake: Missy's blond and blue-eyed like her mother, Mary, but in The Big Bang Theory, she's brown-haired and brown-eyed.