Gitchegumee means "Big Water" in Ojibwe (one of the Native American tribes located in Michigan) and is commonly used to refer to Lake Superior.
At the end of their brief conversation in the airport, the man in the Homeland Security windbreaker says to Clark, "Stay out of my beach community." This is a line from the Coen Brothers' film The Big Lebowski. The line is spoken to the Dude (played by Jeff Bridges), to whom Clark, with his unkempt beard, sunglasses, and cardigan sweater, bears a notable resemblance in the scene.
When the customer is complaining at the boarding gate, the customer is wearing a Hawaiian shirt similar to James Cole in 12 Monkeys. Station Eleven plot is very similar to the 1995 film 12 Monkeys were a flu causes the death world wide.