Character mistake: In Amy's lab, when she is complaining to Sheldon how she gave him the simplest tasks, and that they're still not done, Sheldon replies with how Einstein failed math because he wasn't challenged, and that it is the same case with him. Einstein never failed math. Sheldon of all characters should know that.
Character mistake: The bird that Sheldon is afraid of is referred to in the scene as a "Blue Jay." In fact, the bird is a Black-throated Magpie. A Blue Jay is a little smaller, has a shorter tail, does not have the darker plumage, and can be quite obnoxiously vocal.
Character mistake: Sheldon says (during Fun With Flags) "But like the flag over Fort Sumter, I'm still here." The Sumter flag was lowered when the fort surrendered to the Confederates. The flag over Fort McHenry was never taken down despite the British bombardment and inspired Francis Scott Key to write the National Anthem about it. Whouldn't a vexologist know that?