Charlotte names the spider Sting after seeing a copy of J.R.R. Tolkein's The Hobbit. Sting is not the name of a spider in the Hobbit, rather the sword Bilbo uses to fight the spiders.
Charlotte's name is more than likely a reference to Charlotte's Web, another story about a clever spider.
When Ethan asks Frank why he carries a nail gun while he is an exterminator, Frank answers "protection". The nail gun is likely a reference to Arachnophobia (1990), another movie about carnivorous spiders where the main character finishes one of the creatures off with a nail gun.
First film directed by Kiah Roache-Turner to be set in the United States, as opposed to his native Australia.