Early in the episode, when Sheldon and Mary are next to the kettle, Sheldon's bow tie disappears and reappears.
George's shirt changes from when he greets Jim at the door to when they are in the kitchen getting a beer.
Both George's and Missy's outfits change between the scene in the kitchen to the scene when Missy sends them grocery shopping, yet there has been hardly any passage of time between these scenes.
Georgie told Jim in the Season 6 finale that Sheldon and Mary were in Germany. But in this episode, he didn't know Mary was away until George told him.
Missy's Family Chore Chart only has dish washing assigned twice per week.
As Sheldon points out, he was not interested in sightseeing. Thus, he places Schwetzingen Palace in Heidelberg (10 miles away) and the pictures of Heidelberg Castle get mixed up with Cochem Castle (more than 110 miles away).
Sheldon calls Dr. Linkletter to ask why he never told him there were 26 dimensions. This is a callback to Pilot (2007) of The Big Bang Theory (2007), where they mentioned 26 dimensions existing. However, there it was established that Sheldon had only recently come up with the idea that these additional dimensions exist. Leonard declared that Sheldon invented them to "make the math work out" for what was on his board at that particular moment, about 25 years later than this episode's time setting.