When Bender leads the penguin charge on the hunters, his speech, "we will fight them on the beaches, we will fight them on the glaciers", is taken from Winston Churchill's famous speech during World War II.
The tanker was thought to be (unlike The Professor,) virtually leakproof due to its 6,000 hulls, which later are all breeched. This is obviously a reference to The Real Titanic incorrectly being deemed unsinkable, one reason being its 2 hulls, both breeched on its maiden voyage, leading partially to the sinking.
The song that Bender sings while flying the ship upside down while drunk "Oh Greenland is a barren land, a land that bears no green. Where there's ice and snow, and the whalefishes blow..." is called "Greenland Whale Fisheries" by the Pogues.
When Bender is thrown out of the ocean on Pluto by a whale shark, he whistles one of Star wars' R2-D2's iconic dialects.
When Bender resets after being shot, he scans Leela and identifies her as a human, not as an alien as she is suspected to be.