Doing It for the Art: The story behind the cover of The Nice's Elegy is a prime example. While listening to the album, Storm Thorgerson had a mental image of a desert scene covered with plastic red footballs. He and Aubrey Powell actually went to the Sahara to shoot it. To quote an anonymous poster at Album Art Photos:
"[Hipgnosis] had to take these balls to the Sahara, inflate them, place then on sand dunes as far as the eye can see, repeat this because of the winds moving the balls, remove the footprints as best they could, then take the photo. No CGI. A lot of hard work, but an iconic image."
Old Shame: Thorgerson and Powell deal with this trope imaginatively in their retrospective book For the Love of Vinyl: The Album Art of Hipgnosis. In the introduction to the (nearly) complete list of their covers at the back of the book, they admit that "There are some designs we would rather like to forget altogether"; within the list, these are marked with an icon of a turkey.
Also, every time they mention their pre-Hipgnosis book cover company Consciousness Incorporated, they apologize for the name.