At 9:43 Madeline Wuntch's hand is on Commissioner Kelly's upper arm. When the camera switches to a second angle, her hand is on his shoulder. Then it cuts back to the original angle, and her hand is back in his arm.
The Vulture is referred to as a Captain, yet he wears the badge of a Detective. Later he mentions being a precinct Captain, so this was likely a costume issue.
Wuntch mentions that she has been awarded the NYPD Combat Cross, yet she does not wear this important medal (green ribbon bar) on the "rack" above her shield. Likewise, Holt claims he has the Medal for Valor (dark blue ribbon bar) but does not wear this medal above his shield.
Wuntch's commendation bars lack the black "WTC" commendation, given to all NYPD officers who served on or in the wake of the 9/11 attack on the World Trade Center. Holt, Terry, and most high-ranking officers seen throughout the series have it. Wuntch has served in the NYPD at least as long as Holt, so she should have received the WTC bar. Also, most of the commendation bars Chief Wuntch wears are not issued by the NYPD.
Part of Jake's plan hinges on the Vulture being the primary investigator on CJ's fake kidnapping. The Vulture's entire MO (up to and including his nickname) is that he does not investigate crimes until they are almost completely solved by others, only swooping in at the last moment to take the credit.
Jake says that he hasn't spoken to CJ in three years. It had only been about two and a half years since CJ's previous appearance in The Overmining (2016). Even if the two hadn't spoken off-camera since then, it would still not have been three years.
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.