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)
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.