After "Sweet" Clyde Dixon solves the task of how to get everyone back to their original bodies, he says "Q to the E to the D", meaning Q.E.D., which means that his Inversion Theory is possible.
This is similar to the plot of the Stargate SG-1 episode "Holiday" (e.g. involving a machine that switches bodies, but can't switch back using the same two people)
This is another time bender says he is 60% or 40% something, this episode being storage space.
"What happens in Cygnus X-1 stays in Cygnus X-1" is reference to the fact that Cygnus X-1 is a black hole, which would have gravity so strong nothing could excape. Also it is based off of "What happens in Vegas stays in Vegas"