The giant anthills are real and were an accidental discovery while filming Hermit Bob in the woods. Jim liked them so much he added the scene and dialogue spontaneously.
According to Jim Jarmusch, Iggy Pop asked him prior to shooting what the backstory for his zombie character was and Jarmusch explained he and his girlfriend were killed on his motorcycle in 1973 after leaving a Blue Öyster Cult concert. Iggy Pop actually performed with Blue Öyster Cult and Kiss in 1973.
When the three cops are driving down the road toward the cemetery, Adam Driver's character leans out the window with a machete to cut off the head of one particular zombie. This zombie is dressed in the same clothes and with the same hair as Bill Murray's character in the 2009 zom-com Zombieland.
When Adam Driver pulls up at the diner in his small red smart car, the sounds are taken from a Star Wars vehicle sound effect. Later, when he hands the keys to Tilda Swinton, she notes the Star Wars key chain. Both of these scenes reference Adam Driver's involvement in the Star Wars movie series as the character Kylo Ren.