When Serena arrives, she says she was Captain Ross' last hire and came from Chicago. The NYPD does not confer hiring authority on Captains, and sworn officers hired are placed into patrol to start, not the detective bureau.
It would take Serena at least a decade to go through the NYPD system and hierarchy to make detective and then become eligible for Major Case. There would be several dozen detectives already in line for the limited slots and she would have to wait for them to be hired, retire or die before she could reasonably expect to be assigned to that unit.
The detectives say the new Arabic country is called (phonetically) "Poon" Land. There is no "P" sound in Arabic.
A group of police bagpipers play the Christian hymn "Amazing Grace" for Captain Ross's funeral. Captain Ross was Jewish.