When Sheldon mentions in the opening voiceover that California was the first state to require catalytic converters, it is the Oregon Senate chamber that is pictured on the screen.
When Sheldon is playing Oregon Trail on his computer, the music for the Kansas River Crossing can be heard. While Sheldon does arrive at the river crossing in question, as can be seen at about 3:50, the music is already playing as he approaches the river, whereas, in the game, the music only starts playing once you have arrived at the river crossing, but not in the travel screen.
In Dolomite, Apple Slices, and a Mystery Woman (2018) Sheldon snidely dismisses geology as "not real science", and yet his hero Professor Proton's Multi-Lab box has geology displayed prominently on its cover.