Brooklyn Nine-Nine: 10 Things That Must Happen Before It Ends
6. Kevin Solves A Case
Kevin Cozner - that joke name still gets a laugh every time - has undoubtedly been a useful presence in the series. In the beginning, he was stoutly against the Nine-Nine because of his hatred of the NYPD, but now he's a regular there. This is a very well-seeded narrative that would come full circle if Kevin were to play a significant role in solving a difficult case, despite not being a detective.
There's no doubt that Kevin is a great critical thinker. The show has made him out to have a genius-level intellect very consistently, so it would be within the realm of possibility to see him use this to help the Nine-Nine out. There have also been plenty of moments where he's been heavily involved with a case, either because it involves him or his husband, but finally seeing him use his smarts to solve one would deliver some great fan-service.
However, it would do more than give the fans a nice moment, as it would pay off the character's journey. He started as a stand-offish critic of the Nine-Nine and coming round to their side enough actually to solve a case would perfectly conclude this arc.