The old name of Tampopo's restaurant, when she first meets Gorô and Gan, is Rai Rai Ken. Years later, when the first authentic râmen-ya opened in New York City, it took its name from this scene.
Many elements of the film closely parallel a classic Western. Goro is the mysterious stranger who rides into town; he saves the pretty girl from harassing bad men, and even has a brawl with another man at the edge of town.
When Goro is washing his truck he dumps a bucketful of water on it but uses no soap. This is actually a washing ritual that is part of the Shinto religion.
The exhausted woman who is married to the running man is suffering from "karoshi," which means "worked to death." Many people suffer from overwork in Japan, and many more die from this condition.