If you watch closely, after Fry is leaning on the chair just after the countdown to ten reaches zero and he loses his balance, they cut to a close-up of the chair's legs falling over. You can see Nibbler's shadow cast on the wall in front of him. This was however retroactively added to the first season DVD. In the original pilot premier Nibbler's shadow was not present.
In the Slurm ad, there's a condition for the competition which fills the screen and is written in Alienese. It says "the following species are ineligible: Space wasps, Space beavers, any other species with the word space in front, space chickens and the elusive yak-face."
When Lrr and Nd-Nd are dining at the park, trying to get in "the mood", Lrr gets very agitated at his wife. He jumps up and screams to her "One of these days, Nd-Nd, bang. Zoom. Straight to the third moon of Omicron Persei 8." This is a spin-off from the 50s TV show The Honeymooners, in which one of the characters says almost the exact same thing to his wife, Alice.
On the DVD commentary, David Cohens mentions that Matt Groening's favourite line in the entire show is 'You watched it, you can't unwatch it. Stay tuned for more Tales Of Interest' spoken by Maurice La Marche as the narrator for this episode. Groening confirms this himself.