The comment of "I'll have what she's having" by the woman in the restaurant when Leela is crying in pain from having her hand bitten off by the clam is a reference to the famous "deli scene" in When Harry Met Sally....
When Fry and Leela are swinging, the other characters, frozen in time, are in the same position as the plastic monkeys from the old toy "Barrel of Monkeys."
Fry jumping from the Vampire State Building and travelling in time is a reference to the events of Men in Black 3.
Fry and Leela getting married while stuck in a single moment in time is similar to the Doctor Who episode 'The Wedding of River Song'.
As Fry is falling from the Vampire State Building, he sees the time is 6:25 but his watch says 7:03. Since the Time Button operates for ten seconds at a time, this 38 minute difference means that Fry used the Time Button 228 times to make the arrangements to propose to Leela. (This assumes his watch was in sync with the clock on the building.) The last of the 228 times was to prevent her hand from being bitten off by the clam at the restaurant.
EASTER EGG: In the first scene of the episode, you can see that sunken cart in the crater in which that appeared in the second episode of season 1 as the Planet Express Ship heads for the parking lot.
The moon-headed, balloon sculptor is a tribute to the very first science fiction film, Voyage dans la Lune (A Trip to the Moon) (1902). It was a silent film produced, written, directed and partially acted in by French director and master magician Georges Melies. It's screenplay was inspired by Jules Verne's' From the Earth to the Moon (1865) and H. G. Wells' First Men in the Moon (1901). The movie satirized the conservative science community of that decade and was made on a huge budget, for the time, of 10,000 Francs. His gamble paid off as the film was very popular. It is also known for being one of the earliest films pirated.