Bernadette's legs change position while she plays as a catcher when Howard is doing ball practice.
Bernadette wasn't holding the measuring tape straight. The way the measuring tape was let to sag adds another six inches to the actual measurement. The arc length of a similar problem of the length of a cable of a suspension bridge is a standard calculus problem most engineers know.
Sheldon says that the 13 American colonies got together and created the U.S. Constitution. The original 13 colonies created the Articles of Confederation, the first American constitution that lasted for about a dozen years. The 13 American states then created the U.S. Constitution, a distinction that the know-it-all Sheldon should have known.
When Sheldon gets bored at the stadium, he suggests going "across the street to Disneyland." While both Disneyland and Angel Stadium are in Anaheim, they are not across the street from each other: the stadium is about two miles away from the theme park.
In his speech at the stadium, Howard says he is a scientist and the pitch will be delivered by science. Howard is in fact an engineer, not a scientist, and the pitching machine is an engineering solution. Engineers use science to solve real-world problems. That distinction has been a cornerstone throughout the series and the very point of countless gags.
Despite his lactose intolerance, Leonard's pub burger had cheese on it.
Sheldon asked for one of Amy's french fries. It has been stated many times before that Sheldon is a germaphobic and wouldn't eat food from other people's plates.