Bugs Bunny hides in the lamp and says, "I am Genie, the light brown hare," which is a play on the song "Jeanie with the Light Brown Hair," written by Stephen Foster in 1854.
Very fancifully rendered desert scenes, as befits the mid century vibe. Similar to many Roadrunner Coyote cartoons of the same era.
Pismo Beach, CA is indeed famous for its tasty clams. However, oysters (not native to Pismo Beach) produce pearls, not clams.
Bugs mentions Albuquerque, NM and La Jolla, CA. He mispronounces "La Hoya" (the Spanish pronunciation of La Jolla) as it is spelled, "La Joh-lah." A common mistake of non-native Californians unfamiliar with the state's Spanish heritage.
Sasparilla, which is mentioned by Hassan, is a soda drink made from the sasparilla root. Similar in flavor to root beer, it is still a popular beverage in parts of Asia.