Like every Pixar movie, it contains references to other Pixar films (both short and feature-length). Also plenty of references to NASCAR.
The name McQueen itself is a reference to Glenn McQueen, a senior animator on early Pixar films who died of cancer in 2002; Lightning is named as a tribute. The Pixar staff takes pains to point out that it wasn't, as is commonly thought, a reference to Steve McQueen, he of the famous car chases.
Lightning himself uses Lightyear Buzzard brand tires, and the Lightyear blimp can be seen at races. This one is a twofer: a hark back to Buzz Lightyear and a pun on Goodyear Eagle tires. Additionally, the Dinoco brand is the name of the gas station Woody and Buzz get stuck at, while also a pun on Sunoco, the current brand of race fuel used by NASCAR. And Lightning's number, #95, is a reference to the year Toy Story was released..
While he and Lightning banter over who deserves a major award, Francesco emphasizes that he is notfra-gee-lay.
An automotive version of Takeshi's Castle appears on a television set when the cast arrives in Japan.
Visually, the Death Trap inside of Big Bently, and the way that Finn, Holly, and Mater escape from it, is very similar to the climax of The Great Mouse Detective - itself inspired by the clock tower chase in The Castle of Cagliostro, a movie often cited for its great spy action and excellent car chase sequence.