Continuity mistake: When Sheldon is putting his mittens on at the table he his seen putting the first one on and the second one is on the table, the shot changes and the mitten is no longer on the table. He raises his hands and both hands have mittens on them.
A Computer, a Plastic Pony, and a Case of Beer - S1-E12
Continuity mistake: When we see Sheldon in bed at the start he's either flat on his back or on his side depending on the shot.
Continuity mistake: When Sheldon and Missy are sitting at the table, Missy puts a paper in the basket in front of her. A couple of shots later when she says "sounds right" the paper has disappeared. In the next shot it reappears, in a different position than it was before.
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.
Continuity mistake: In this episode, the voice over version of Sheldon states that he never got his drivers licence. However, in series 12 of The Big Bang Theory, he tells Amy that he got his drivers licence 2 years ago.
Continuity mistake: Younger Mary's a blond with blue eyes whereas on The Big Bang Theory she has brown hair and brown eyes.
Continuity mistake: When Georgie is fighting on the football pitch he is pulled off the other kid and stumbles back. Camera changes and he is seen being pulled again and landing on the floor.
Answer: It is shown numerous time in The Big Bang Theory and Young Sheldon that Georgir Jr is not the smartest kid going. They simply tell him Sheldon is getting a hair cut as it is believable. It's also shown that Sheldon has had the same style hair cut since he was 5. Since he is 9 in Young Sheldon, he's had the same style for over 4 years already. Easy to overlook that he hadn't actually had it cut after that long.