Gene mentioning putting keys in a bowl and Sigourney Weaver is likely a reference to The Ice Storm (1997). A character played by Kevin Kline (Mr. Fischoeder) is having an affair with her character.
Burger of the Day: The Corn Identity Burger (Comes with corn relish). This is a reference to the film The Bourne Identity (2002).
Store next door: The Quick and the Bread bakery. This is a reference to the film The Quick and the Dead (1995).