The professor admits to numerous violations of safety and minimum wage laws. Considering that the labor we have thus seen in this franchise is both perilous as well as done in terrible conditions, this is a mild surprise, that pro-worker laws even exist. (In any case, in a later episode, the professor remarks that the crew has been suing him; is this the origin of those lawsuits?)
Zap Conquest: single handedly defeats the Retiree People of the Assisted Living nebulae. The hero we need?
Class division on ship: the professor, Hermes, and Dr. Zoidberg (an intellectual, state employee, and medical doctor), all live in posh conditions in first class while the crew (the working class) live in “the fiesta deck”, which is even below the “bowels of the ship”.
When the crew is in the elevator descending, the various levels reflect the class composition of the inhabitants: First Class (wealthy, professionals, politicians, etc.), Second Class (middle class tourists), Steerage (lower-middle class rural strata), Laundry and Bowels of Ship (working class).
Fry’s fake relationship with Amy and Lela indicative of a fraught, clichéd heteronormativity; hence, the references to “Three’s Company” and the sitcom dilemma. Hints at the artificial nature of romance (reinforced when the nebulae which Fry and Lela ‘wish upon’ is sucked into black hole).
Hermes’s Past: while at the Olympics, a little kid rushes onto the field and tries to limbo, but his spine couldn’t “go that low” and he breaks his spine and dies. Until later in the episode, when Hermes must limbo to save the others lives, he had a phobia of limboing since it reminded him at that child.
Zap promotes Kip opportunistically to avoid blame for crashing the spaceship. Reveals that Zap has no issue in handing off rank or prestige as long as it clears him of wrongdoing.
Later on, it will be revealed that the countess’s diamond wristband is fake. A jab at the fakeness of the upper-middle class. This is appropriate since the countess, as a robot able to transform into a yacht, has a body literally commoditized into the ruling social strata, so this added layer of artificiality rams home the point that the ruling class is illegitimate.