As Sheldon describes the first episode of Star Trek: The Next Generation (1987), he makes it seem as though Wil Wheaton's Wesley Crusher appears right away. Wil didn't make his first appearance until around the 33.5 min mark.
Sheldon states that Wil Wheaton is the only person he knows that has been immortalized in 1/16 scale. This is not true because he also knows Brent Spiner, who was also on Star Trek: The Next Generation (1987) and his character was also made into an action figure.
During the opening filming of 'Fun with Flags', the camera that Sheldon and Wil are addressing is several yards to Amy's left, rather than the one she is supposed to be filming with.
Throughout the episode, Amy complains that Wil was rude to her, when in fact all he said was that Amy was being a "pain in the ass". Amy was far ruder to Wil than he was to her and she should have apologized to him.