Zorro - During Claw-Plach Zoidberg cuts a 'Dr Z' in Fry's shirt.
Star Trek: The Original Series episode "Amok Time" - The entire episode, particularly the ritual arena combat between Fry and Zoidberg, has close correlations with the episode.
Cyrano de Bergerac - Fry hiding in the shrubbery and giving tips to Zoidberg while Zoidberg romances Edna is a reference to "Cyrano de Bergerac", a play written in 1897 by Edmond Rostand that was made into at least one mid-20th century movie, and was the basis of Steve Martin's movie "Roxanne".
The title comes from a lyric in the 1959 Dion and the Belmonts song "A Teenager in Love".
In the gym scene, Zoidberg says he is going to work out with "the nautilus", and goes to play basketball with a nautilus-like alien. The company Nautilus, Inc. produces exercise equipment.
In the gym scene, one of the "dirtiest, but subtlest jokes ever on Futurama" (as described by David X. Cohen on the DVD commentary) is seen: the Kegelcizer machine.
When Edna kisses Fry, her facial tentacles wrap around his head in a fashion which is reminiscent of an attack of an Illithid or Mind Flayer from the Dungeons and Dragons game series; illithids, like Decapodians, have four tentacles around their mouths, and wrap them around heads to extract the brains for consumption.
The national anthem of Decapod 10 is the same music heard during the fight scene between James T. Kirk and Spock from the Star Trek: TOS episode "Amok Time". The Song was Titled The Ritual / Ancient Battle / 2nd Kroykah. Several elements in this episode, such as Decapodian mating season and the ritualistic battle to the death also mirror plot details from that particular Star Trek episode. Also the traditional Vulcan lirpa-weapon used in kal-if-fee is shown as one of the weapons Fry can choose from. Claw-plach also sounds a lot like Qa'pla, the Star Trek Klingon word for "Success." This entire sequence was used earlier on The Simpsons on the season five episode Deep Space Homer when Barney and Homer train to be astronauts.
When taking bets just prior to the Claw-Plach fight between Zoidberg and Fry, Bender refers to Zoidberg as "The Great Red Hope". This is a reference to "The Great White Hope", Jim Jeffries, who, in 1910 fought Jack Johnson, the first black heavyweight boxing champion, in a symbolic racial competition.
The restaurant "Red Primate" is a parody of Red Lobster.
Bender's story about how he became known as "Honest Bender" is a reference to a similar story by W.C. Fields in "Six of a Kind".
During the Claw Plach fight, after Fry refuses to kill Zoidberg, Zoidberg cuts off Fry's arm. Angered, he attacks Zoidberg with his severed arm while swearing at him. The part where Fry uses profanity has been removed out of various syndication.