When Sheldon names the closest stars in ascending order of distance, he misses Alpha Centauri B (which in orbit with its close binary, Alpha Centauri A alternates between the second and third closest stars - after Proxima Centauri) Also Sheldon really should have started with our own Sun which of course is also a star and by far the closest.
When Amy is online to Sheldon on their laptops, she looks to her right when, from the viewer's standpoint, he is sitting to the side. This erroneous as Sheldon would simply be directly in front of her on her screen.
Sheldon refers to Leonard being jealous of his relationship with Amy. However, "jealousy" is not wanting somebody to have something which you have. Sheldon is talking about "envy" (wanting something which somebody else has) and being a stickler for correct use of language, Sheldon would know that.