Oh, then that certainly is actionable. If animals are crawling inside, she's harboring vermin. Also, if you document the roof material on your deck, you might be able to work it as a hazard to you--things are routinely falling off on her property and pose a danger to someone on yours.
Having a large hole in a roof is a lot different-sounding than just saying you have to spend two minutes a couple times a year after a storm and are more worried about the perceived impacts on your property value. Two minutes a couple times a year sounds like minor debris after an unusually strong seasonal storm...when I lived in the Midwest, we'd regularly spend 30-60 minutes cleaning up branches, leaves and/or chipped roofing materials (slate roof) nearly a dozen times in some years, so to me, a few minutes 2-3 times a year seems pretty minor. Has this been going on for a while? It would take a long time or a couple of very brutal storms to rip that kind of hole in a roof like that, and like you, I'm surprised your neighbor isn't apparently having severe water intrusion issues.
Speaking of water...with moisture comes mold. Depending on the situation, you could also have cause for action if you think your neighbor's lack of repairs is causing air quality problems for you due to toxic mold spores.
Basically...at least in the US, you can't do much/anything if your neighbor is offending your aesthetics or simply not being as meticulous as you would be (unless, of course, the aesthetics are in violation of neighborhood covenants, codes and/or restrictions). But you would have actionable cause if whatever your neighbor is doing is leading to health/safety/welfare issues for you/the neighborhood. Harboring wild animals (including birds--if they produce excessive droppings on your property, that's a health issue), mold, or maintaining an unsafe condition (debris regularly falling on your property) are all legitimate claims you should be able to make to the appropriate local authority. Hope this helps.
The shingles that are coming off are mostly coming off whole, so that's why it's easy to clean up (asphalt shingles). The pile that I collected this spring was about a foot thick and probably contained 30-40 shingles.