When Mary is talking to Missy and Georgie about Sheldon having no friends, the potatoes she is peeling keep changing shapes.
The FBI agent states, "someone living at this address recently called a mining operation in Canada and tried to buy uranium". In The Big Bang Theory (2007), Sheldon's mother already explained Sheldon tried to "buy yellowcake from Chad", not Canada.
The book Sheldon checked out from the library would not have had the card with the names of the people that had previously checked out the book. The library would have kept this card when Sheldon checked out the book.
In this episode (as well as others from this show and The Big Bang Theory (2007)), Sheldon referenced the Dewey Decimal Classification System. However, by the 1980s, most US libraries had converted to the Library of Congress classification system.
George Sr. asks Tam about the origin of his name, and Tam replies, "Vietnamese". George Sr. then mentions that he spent time there, in the Army, and asks Tam if his mother's name is "Kim Lee". Kim Lee is a Korean, not Vietnamese, name.
In this episode, and in The Big Bang Theory (2007), Sheldon speaks of being contacted by Homeland Security when he tried to purchase uranium. The Department of Homeland Security did not exist until after September 11, 2001.