The music during the fight between Fry and Zoidberg, identified as the Decapodian National Anthem, is the "danger music" from Star Trek (1966), most notably played during the battle between Kirk and the Gorn, and of course the fight between Kirk and Spock in Amok Time (1967), which this Futurama episode is a spoof of..
The first top weapon offered to Fry at the beginning of his Claw-Plah with Zoidberg is Vulcan Axe. Similar axes were used during Kirk-Spock fight at Amok Time (1967), that this episode largely spoofs.
A still of Zoidberg, in the scene when he's explaining Claw-Plach to the crew, is infamous on the Internet as part of the "Why Not Zoidberg?" meme.
Fry, Leela, Bender, Zoidberg, and Edna eat at Red Primate, a reference to the restaurant chain Red Lobster.
The window scene where Fry coaches Zoidberg is a reference to a similar scene from "Cyrano De Bergerac".