Ani tells Kate she looks like the Terminator bitch with her sunglasses. Later, when she takes her glasses off at the beginning of the final assault, her left eye is red, as is the left side of her face, as a clear nod to this legendary killer.
Members of Japanese all-female hard rock group BAND-MAID appear in the movie as themselves.
The TV show Jojima is watching is a Sci-Fi movie/series know as Message from Space: Galactic Battle (1979) from the late 70s.
The aerial shots at the beginning of the movie are actually Osaka City. The first approaches from the south with the Harukas building and the Tennoji area. The second shot is of Osaka Bay with the Ferris wheel visible near the Osaka Aquarium. In reality these areas are not near each other. It would take between 20-40 minutes to travel from Tennoji to the Aquarium depending on which train line you took.
In Kate's sharpshooting scene: the anime shown on the building wall is Tokyo Ghoul: Root A (2015).
The story of Kate also owes a nod to the film noir classic D.O.A. (1949) and the remake, D.O.A. (1988). In both, a man is poisoned, and he searches for his killer in the time he has left.
In the opening of the film, Kate (Mary Elizabeth Winstead) enters a sea-side warehouse area in Osaka, Japan. Upon approaching two Japanese men she asks them "where Shitennoji Temple is". They tell her, "it's back the way you came" as if the Temple is in the neighborhood. In reality, Shitennoji temple is nowhere near the sea or the warehouse area. If she were to walk back the way she came, it would take several hours to get there on foot. (They are obviously not giving her specific directions; as they are Yakuza guards they are implying that she needs to get lost.)