During the bathroom scene, Gaius Baltar is actually whistling the theme from the original Battlestar Galactica.
Baltar whistles part of the "Top Gun (1986) Anthem" during the scene where he is speaking with Gaeta from within a bathroom stall.
47,958 survivors as listed previously on Laura Roslin's white board. The number is not displayed or spoken but the count doesn't change during subsequent shows.
The title references the postulation that any person can be connected to any other person in the world through up to 6 social connections. It was popularized by the game "Six Degrees to Kevin Bacon" where you attempted to connect an actor to Kevin Bacon by connecting that person to others who were either related or had been in movies with Kevin Bacon. Incidentally, Mary McDonnell (President Laura Roslin) was in The Closer with Kyra Sedgwick, Kevin Bacon's wife, connecting BSG in just two "degrees."
Gaeta's enhancement of the photograph that was meant to implicate or exonerate Baltar is a similar plot device from the film No Way Out, when a Pentagon technician was tasked with enhancing a Polaroid negative that was found at a crime scene, under the nervous watch of the person who is in the photograph.