The Beer & Brawl sells Fudd Beer, as well as Laramie High Tar cigarettes.
Before Lurleen's performance of "Bagged Me a Homer" at the recording studio, Bart and Lisa argue over the women Homer has had in his life (which are all brand names of foods, like Sara Lee and Aunt Jemima). This footage was included in a promo of the episode and can be found on the DVD, but the full scene is not.
In this episode Moe believed that Fudd Beer was banned for blinding hillbillies. In Rednecks and Broomsticks, several Springfield residents are blinded by the moonshine-infected water supply (which is blamed on the Wiccan girls in the woods).
Homer's flashbacks of his love life before he met Marge included getting slapped in the face by a girl during Spin the Bottle and an unnamed teen girl dumping Homer by saying, "Thanks for dinner!" sarcastically and driving off.
KUDD Radio's slogan "Don't touch that dial, you've got KUDD on it" is likely a reference to San Jose radio station KOME. KOME (pronounced on air as "COME") was known for sexually suggestive catchphrases; such as "Don't touch that dial, it's got KOME on it!," "K-O-M-E all over your radio dial," "Wake up with KOME in your ear," and "The KOME spot on your dial."
'Fudd' is most likely used because it is almost 'Duff' backwards.