Jake says he's allergic to bees but his reaction from being stung is just a scratchy throat, however in previous episodes it was stated that he is deathly allergic to bees and wasps and he could die if stung.
When leaving the Lake house, Terry tells Jake he watched the show Jake had been talking about and loved it. However, it is repeatedly stated there is no WiFi, so he would not have been able to.
At least a year after his birth, baby Mac has actually shrank since he was last seen in the season 7 finale.
At the end Raymond says he called Kevin to resolve their issue. Multiple times it was explained that there is no reception or WiFi at the Lake House. However the lake house could have had a land line phone, just the sort of traditional technology that Captain Holt would have.
Terry and Jake try to get Raymond and Kevin back together by having them look for a corn crake. Corn crakes are native to Europe and Asia and are not commonly found in North America. However, they are extremely rare vagrants in the Northeastern United States. Kevin even mentions this in the episode.
The chess board in the sitting room is set up incorrectly with black's king and queen reversed. This isn't a mistake Holt or Kevin would make due to their rigid attention to detail, especially for anything considered to be scholarly in nature such as chess.
Near the episode's end, Jake shows both Amy and Captain Holt the corn crake's call on his phone. It is repeatedly stated throughout the episode that there is no cell phone reception or wifi at the Lake house.
Holt and Kevin absolutely butcher the German pronunciation of "Das Doppelte Lottchen", the title of the original novel by German author Erich Kästner that The Parent Trap (1961) was based on.