In Riot On Set, Gwen mentions that she had a job at the petting zoo and she had to clean up after the goats. In the same episode, Duncan, while acting, mentions a goat that his character had in their youth.
The goat appears very briefly in Owen's animation form during The Aftermath: III. When Owen is mentioning all the bad things he's done, he mentions stealing his Uncle Max's toupee and gluing it to a goat's backside at a petting zoo. It only appears in cartoon form.
In Walk Like An Egyptian - Part 1, the goat is a prize that is awarded to Team Chris Is Really Really Really Really Hot for coming in second place in the pyramid challenge. The goat appears to be quite aggressive because as soon as Chris introduces it, it headbutts Tyler.
In Walk Like An Egyptian - Part 2, Team Chris Is Really Really Really Really Hot is able to perfectly balance their team on the goat despite its small size. The goat is able to move the group across the desert and they are the first ones to make it to the Nile River. The goat seems to have a very good relationship with Alejandro, as it jumps into his arms while they paddle across the Nile. Since the team is able to keep the goat with them during the entire challenge, the team is safe from elimination.
In Slap Slap Revolution, Chris orders a vicious, rabid goat to charge the contestants. However, it encounters one of the local goats, which is much bigger and seemingly more ferocious. In an instant, the small one eats the larger one, then resumes its attack. During the challenge, it attacks Team Victory and Team Chris Is Really Really Really Really Hot. Leshawna helps Lindsay avoid injury, while DJ catches it. He holds it in the air and the goat hits a tree branch that they pass under, and gets left behind.
In Aftermath: Revenge of the Telethon, the goat is seen in a segment called "DJ's World Of Animals." DJ tries to pet the goat, but it ends up hurting itself from trying to break free of the cage. Once Blaineley, in an attempt to raise money for the show through ratings, sets them free out of their cages. All of the animals attack everyone in the studio, with the goat ultimately attacking the camera and Geoff.
In Brazilian Pain Forest, a goat appears on the plane full of animals, which the second set of contestants ride on. After Taylor decides to quit the game, she kicks the goat. Seconds later, it takes revenge by headbutting her.
In Darjeel With It, a goat appears on the train car ahead of the Best Friends. When Devin tries to tell Carrie his feelings for her, a goat interrupts the moment by headbutting him.