All of the cast members playing vampires wore wigs that were a mix of human, yak, and goat hair, in order to make them look wilder.
According to the script, Eve (Tilda Swinton) is 2,000 years old, and was the Druid matriarch of a Celtic tribe. Adam (Tom Hiddleston) is 500 to 600 years old. Writer and director Jim Jarmusch decided that Adam and Eve would be aware of each other's true age, so he argued they have no reason to state it in this movie, but simply informed the cast members of the age of the characters. In an extended version of the nude scene, shown in the DVD special features, Adam and Eve do talk about her Druidic connections.
Christopher "Kit" Marlowe (Sir John Hurt) mentions writing Hamlet, and ghostwriting for William Shakespeare to have an outlet for his work. The real Marlowe died under mysterious circumstances at the age of twenty-nine, a few weeks before the publication of Shakespeare's first known play. The Marloweian theory, which is considered fringe by a vast majority of scholars, suggests that he faked his death, and adopted the nom de plume "William Shakespeare".
The white dwarf that Eve (Tilda Swinton) mentions to Adam (Tom Hiddleston) while driving across the city is the star called BPM 37093, also known as Lucy (named after The Beatles song Lucy in the Sky with Diamonds). Its nucleus is cooling down, which makes its core pulsate like a giant gong.
There was some action in this movie at first. But when writer and director Jim Jarmusch was asked to add more, he removed all of it instead.