Nate yelling Genghis Khan's name is an homage to Star Trek II: The Wrath of Khan (1982).
The trio of policewomen appearing near Charlie are a reference to Charlie's Angels.
As Genghis' Khan's henchmen escape, they're shouting "Run awaaaay!" referencing Monty Python and the Holy Grail (1975).
The episode includes several references and homages to Chinese film director John Woo's action movies, including flying white doves, impossible gun fights and tense stalemates, some of which use the same camera shots of some of his movies.