Misery - When Moe picks up David Byrne after he is badly injured, Byrne asks Moe to take him to the hospital. When Byrne asks why Moe drove right past it, Moe ask him "have you ever seen the movie Misery?". The movie Misery is about a writer who is hurt in a blizzard and is taken in (then held captive) by a crazed fan of his work.
Back to the Future Part III - When Bart ropes Homer around the neck to save him from the beavers, it's a spoof of the scene in which Marty is roped by the hands.
When Cleanie comes in he says "My precious". The voice is a reference to the Lord of the Rings character Gollum. Cleany was voiced by Andy Serkis, who provided the voice (and motion capture) for Gollum in the films.
Bart calls Lisa "Crabby Hayes", a reference to the famed Western movie sidekick Gabby Hayes.
The name of the ranch, Dude Ranch, shares the same name with the album, Dude Ranch, produced by pop punk band Blink-182.
The sound of the footsteps when Clara is running across the log do not match her actual footsteps.
Lisa says that the Lazy I Ranch has no radio or TV so they don't have to listen to Homer's song but at the ranch, Maggie is seen dancing to "Oops!...I Did It Again" by Britney Spears on the radio. She could have a Cassette tape or a CD with this song.
Lisa's hat disappears after she first talks to Luke.
Clara does not have a necklace nor a ring until the episode shows them.