What is important about Dave's ethnic identity and his obnoxious appropriation and bastardization of Navajo culture is how openly it is mocked. Dave doesn't look cool, sophisticated, wise, or sexy when he appropriates Native cultures in the show - he looks like an idiot, and his friends tell him so gladly. Dave is the butt of the joke in this episode and it is hilarious.
Along the way Dave suffers robbery and grand theft auto at the hands of some thieves disguised as parade pilgrims and is left penniless on the side of the road. However, Dave continues his quest for clams and ends up bartering with a fish monger. He trades his hideous jacket for the clams and a blanket (It's November in Chicago, he has to have something). But poor Dave suffers again at the hands of deceptive whites, since the blanket is covered in cat hair and he is allergic. Now he is coughing and sneezing in a blanket on the side of the road and has to sell his prized concert tickets for money to get back home. He is then arrested for scalping tickets, get it? - scalping. As he's arrested he shouts, "The pilgrims drove me to it!"
This episode is a comedic masterpiece. It exemplifies the ignorance of non-Native people who appropriate Native identities by showing Dave act like a total ass. Dave ham-fistedly claims ownership of Native history and becomes an instant expert on all things "authentically" Native American in spite of living his life as a privileged white man. For Dave, being Navajo is basically a fashion choice - a point proven by his "Indian" accessories that he only wears when he's in 'Navajo mode.' Dave is only Indian when he stands to gain something from it, be it an edge in the food truck business or a chance to feel superior to his friends, but when there is no immediate benefit in sight he reverts back to whiteness as all cultural appropriators do. Happy Endings poignantly critiques white privilege by making Dave look like a jerk, and encourages the audience to do the same.