I have a few favorite "bad" lenses:
1. Bad image quality
For example, my first zoom lens (Nikon 43-86mm f/3.5) had image quality that was so bad that it soured me to zoom lenses for decades. I sold the lens
For example, my f/8 Holga lens with a micro 4/3 lens mount is a bad lens because it produces images with bad quality. However, the images are not bad enough to scrap this low-cost lens.
For example, I once had a Tokina AT-X 400mm f/5.6 auto focus lens that I loved. It had fast auto focus, low cost, nice design, and good material. However, I could never get a sharp image out of this lens. I used it for few years before I finally replaced this bad lens with a 400mm f/5.6 manual focus Nikkor.
2. Broken
For example, I accidentally dropped the only Sigma lens I ever owned down a flight of stairs. It would have cost me more to repair it than I paid for the lens. I still have the lens and it is still broken.
For example, I have a 1000mm f/11 Nikon mirror lens that has a mirror that has started to de-silver. The images have not yet been seriously affected by the mirror defect. It would cost too much to have the mirror repaired. This bad lens is still worth keeping until its image quality is seriously affected.
For example, I have a Mamiya-Sekor C 180mm f/4.5 lens for my RB67 medium format SLR that is loaded with fungus. I bought it in a lot that contained an RB67 prism finder that I wanted. I could either reject the entire lot or keep the lot with the contaminated lens. I kept the lot. The lens is now safely stored in a sealed plastic bag.
3. Keeps breaking
For example, my 80-200mm f/2.8 Nikon auto focus zoom has a broken auto focus motor that will cost me
$200 or $300 to fix. Even after the lens is repaired, the motor is likely to break again. The lens is bad now but I will keep it because it is a favorite lens when it is working. One day, I may decide to have it repaired.
4. Costs more than the lens is worth
For example, I bought a Nikon 105mm f/3.5 lens that would not focus on infinity. However, since I only planned on using it for close-ups and portraits, I was able to use it in its broken state for years. I finally decided to have this bad lens repaired. Now this repaired lens cost more than the lens is really worth.
5. Has poor design, material, or workmanship
For example, I once owned a Nikkor 45mm GN f/2.8 lens that had great image quality but had design features that I could not stand. The lens was too small for my hands. The focus ring rotated in a direction that was opposite to all my other Nikon lenses. Its ergonomic design problems were too much for me. I sold this "bad" lens.
For example, I received a 28-200mm f/3.8-f/5.6 Tamron auto focus zoom as gift. The lens was built with too much plastic material and was so poorly constructed that it would not mount on some of my bodies. Its image quality was mediocre and its maximum focal length was not 200mm but more like 150mm. Also, the lens also has a variable maximum aperture and I do not like lens with variable maximum apertures. However, after I tried this bad lens for a while, I discovered that it made a very good portrait lens. I also decided the lens was really worth keeping for use on the beach where I would not suffer a great financial loss if it were damaged by sand.