The title is a play on the phrase "Mum's the word."
The scene where Peter beats up a bunch of annoying people while holding in his poop is a parody of a scene from Airplane! where a pilot beats up a mob of religious recruiters while calmly walking through the airport. 
Peter makes a reference to Dick Clark when he argues that you can't die of a stroke, you just get to host New Year's Eve and talk funny.
Evelyn's skirt blowing up over the street grate is a reference to the Marylin Monroe film The Seven Year Itch.
Peter's "In Memoriam" clip of being Kathy Bates' butt double is a reference to Bates' scene in About Schmidt.
When Peter first meets Evelyn, he addresses her as "Cocoon", and says they do not have any rocks to make her stronger. This is a reference to the film Cocoon, in which alien cocoons that resembled rocks where to be placed in a pool charged with "life force", so that the encapsulated aliens would receive enough energy to survive the trip home. In the film, the rejuvenating pool was discovered by three retirement home residents.