Sheldon attempting to write an episode of Star Trek: The Next Generation isn't so far-fetched. The shows Star Trek: The Next Generation (1987), Star Trek: Deep Space Nine (1993) and Star Trek: Voyager (1995) had open submission policies and made their submission guidelines public. Once a script was submitted by a hopeful writer, the producers could determine if the writer understood the shows they submitted to and not only could their script be produced, they could be invited to pitch any other ideas they had as well. This open submission policy started the careers of Jane Espenson, René Echevarria, Ronald D. Moore, Bryan Fuller and Robert Hewitt Wolfe among others. Starting with Star Trek: Enterprise (2001), the open submission policy ended for liability reasons: it was too easy for fans to submit ideas that were already in development.
Sheldon invents the idea of Bitcoin.
An Easy-Bake Oven is spotted in Georgie's place.
Sheldon suggests Dr. Linkletter take his Meemaw to the Holodeck. The Holodeck is a virtual area on the Enterprise, in Star Trek: The Next Generation (1987), where ANY place in time and/or space can be holographically (and physically) manifested & enjoyed as if truly present. Hence, Meemaw could enjoy a fabulous restaurant ANYWHERE in time/space in the Holodeck. Obviously, Dr. Linkletter knows little about the TV series.