Chuck Lorre's Vanity Card at the end of the credits commemorates the passing of frequent guest character Stephen Hawking, who had died two weeks before this episode was aired in the USA.
Although Penny hopes that doing a good job on giving Bill Gates a tour around her work may land her that PR job that she really wants, the PR job is never spoken of again.
The blue shirt Sheldon wears in the "giant panties" scene displays a graphical representation of the Fibonacci Sequence, wherein each succeeding digit is the sum of the two preceding digits i.e. 0112358 etc.
Bob the Builder (2015), which Bernadette watches on TV, was originally broadcast on the BBC. It was then sold to America and broadcast there with American voice actors. The version Bernadette watches has the original British audio track; Lee Ingleby can be heard as Bob instead of his American voice actor, the late William Dufris.
Sheldon shouldn't be so eager to meet Bill Gates. According to Leonard, Howard and Raj in The Toast Derivation (S 4 E 17) Bill Gates punched Sheldon for insulting him about Windows Vista.