When Jake is talking to Jess about the "serial licker" on the loose, his left arm goes from down by his side to up on the window ledge and back again between shots.
The scene of Jake commandeering Jess's vehicle contains alternate takes and lines of dialogue that are incongruous with how those events played out in the first part of the crossover.
Jess interacts with Gina and Captain Holt at the 99th precinct during the day time. At this point in Brooklyn Nine-Nine (2013), the main cast (including Holt and Gina) had been reassigned to the night shift. In fact, the first part of this crossover was The Night Shift (2016).