Sheldon reads from his Star Trek compendium and the first entry states that the Federation was formed in the 23rd century. In the actual Star Trek encyclopedia, the Federation was formed in the 22nd century (2161).
Sheldon tells his mom he is watching "Star Trek: Deep Space Nine (1993), not TOS" (The Original Series). Back in the episode's time-setting of 1992, the show was known only by its original title: "Star Trek". There was no "The Original Series" added to the title until just recently.