The Star Trek (1966) episode shown in this episode is The Return of the Archons (1967), first broadcast in February 1967.
As Sheldon enters Georgie's room, a sign for Farm to Market (FM) Road 794 is seen on the floor behind the door. FM 794 is a real road heading north and south between Gonzales, Texas and Harwood, Texas, about 50 miles east of San Antonio.
This episode explains why in The Big Bang Theory (2007) when Sheldon is involved in a lie he always goes to extremes to add details even when absurd and unnecessary.
A clip of the intro to the show A Pup Named Scooby-Doo (1988) was shown when Sheldon changes the channel. In fact Iain Armitage who plays Sheldon later became the voice of the young Shaggy Rogers in Scoob! (2020) which came out three years later after the debut of the show.
When Sheldon starts to sneak into Georgie's room at night the background music is a takeoff on the theme song from the 1960s television show Mission: Impossible (1966).