Rockets, Communists, and the Dewey Decimal System - S1-E2
Other mistake: As Young Sheldon is a prequel series to Big Bang Theory, this episode is at odds with episode 2-13 of Big Bang Theory, "The Friendship Algorithm," in which Sheldon is unfamiliar with books like "How to Make Friends and Influence People," which he reads in this episode of Young Sheldon, produced nine years later but taking place twenty years earlier.
A Solar Calculator, a Game Ball, and a Cheerleader's Bosom - S1-E5
Factual error: The commentary suggests that Sheldon had the correct solution to problem 1 and merely lost points on the quiz because he didn't show his work. In reality he did the first problem incorrectly. Taking the derivative of (x+2) ^2+ (y+1) ^2 = 13 with respect to x yields: 2* (x+2) +2* (y+1) * (dy/dx) = 0 which implies that: dy/dx = - (x+2) / (y+1) and at the point (0,2) this means that the slope dy/dx is actually equal to - (2/3), not 2/3. It is correct that when using the form y=mx+b at the point 0,2 reveals that 2=m*0+b, or that b=2. So the correct equation for the tangent line is y = - (2/3) x + 2, not y = (2/3) x + 2 as shown in the episode. (00:13:55)
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.
A Solar Calculator, a Game Ball, and a Cheerleader's Bosom - S1-E5
Factual error: In this episode we see George throwing a ball against his bedroom wall. On the wall is a picture of Axl Rose wearing shorts in the pattern of the USA flag. This photo is from the Guns N' Roses appearance at Rock In Rio 2 festival in Jan 1991. The show is set in 1989. 2 years prior to the photo the poster is made from is taken.
A Sneeze, Detention, and Sissy Spacek - S1-E13
Visible crew/equipment: When Sheldon is running away from Mary in the garage, the set lights are reflected in his helmet. (00:18:00)
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.
Jiu-Jitsu, Bubble Wrap, and Yoo-Hoo - S1-E17
Plot hole: Near the start we see Sheldon using physics to try and take down Tam. This completely goes against all of Sheldon's phobias about touching people, especially socks. Even before this episode he has shown his displeasure at the thought of touching people. (00:05:00)
A Patch, a Modem, and a Zantac - S1-E6
Factual error: At the start of the episode when someone is talking at the podium, there's a a periodic table behind him on the wall. On the left of barium, 'Sc' for scandium is there instead of 'Cs' for cesium.
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.
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.
Revealing mistake: We see George hit some trash cans while driving, then a while later later he hits some different ones. However the clip we see the second time is the first clip, reused.
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.
Visible crew/equipment: When Missy runs through the house at the start the stage lights are reflected in her sunglasses. (00:02:25)
Answer: Some people just have a dislike for someone that can't be explained. Could be as simple as the way he's dressed.