When Bea and Paul enter the restaurant, the door stays open behind them. When they make their way back towards the door after the owner tells them to leave, it is closed.
SPOILERS:During their only encounter, at the restaurant, we learn that Bea and Will knew each other intimately when they were kids (she later reveals they were 13). At one point, Bea playfully taps the brim of Will's hat, and says something along the lines of, "Still wearing that hat, eh?" The hat, which is supposed be a nearly 15-year-old favorite hat, is stark, bright white, and looks brand new. First of all, the guy lives in a forest. A white hat would last maybe a week. After 10+ years, it would at least have some visible signs of wear, but this hat had none.