In Season 1 Episode 14, Terry says if he could be any vacation he would be "Lake Trip". In this episode he seems really worried about the trip and all the things that can go wrong and the diseases etc you could catch.
On the drive up to the cabin, Jake mentions "bonfires and s'mores" as one of the activities he has planned. It is later shown that Jake did not bring any food with them because he assumed they'd be awesome at fishing and could catch their own. Even if they'd been excellent fishermen, there's no way they could have caught chocolate bars, graham crackers, and marshmallows.
Amy's book light is supposed to be magnetic, yet it attaches directly on to her clothes.
When Amy is informed that a little girl said she would use her shoulder light to break the world record for speed reading, she scoffs at the notion that a little girl would "take down Yuri Jurgonav." The actual world record holder for speed reading is Howard Stephen Berg, who in 1990 set a record of 25,000 words per minute.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
When Terry is "driving" Charles and Jake to the cabin, the gear selector can be seen in the "park" position.
About 8:40 in, Captain Holts is reciting a URL and repeatedly says 'backslash' instead of 'forward slash'.
Even if it was an unseasonably warm November and the temperatures weren't getting down to freezing every night as they normally do, the leaves would not still be green this late in the fall in this part of the country.
After he has eaten the bar Charles gave him, Jake declares that it has been "digested." Digestion is a process that takes several hours as the body breaks down food and absorbs its nutrients. Jake meant that the bar has been eaten.
Jake asks Terry if they're going to set off the fireworks by shooting at them. Shooting fireworks would not set them off. As a police officer, Jake should have more knowledge on the workings of firearms and explosives.
The criminal that Jake and Charles arrest tells Jake that he has fudge on his cheek. The breakfast bar that Jake had eaten did not contain fudge. The substance on Jake's face could only have been a chocolate chip.