or even simply the appearance of feathers - they are just elongated scales? How did it get from a scale to a feather?
no, feathers bear more similarity, structurally and chemically, to hair than they do to scales. birds have two types of feathers, the small round reptilian ones (bottom of the foot), and the flat rectangular avian "scutes" (top of the foot). scutes evolved from feathers, not the other way around. there's actually a good selection of dinosaurs specimens with flight feathers on their feet.
Now the main problem is that we have not observed ANY such (similar)mutation in higher order animals such as mammals, birds, reptiles etc.
i'll avoid making a rhetorical point, and contribute something of interest. there's no reason why mammalian hair (as opposed to early archosaur "hair") can't form feathers or scutes. take for example the pangolin, a kind of anteater. they are covered in in overlapping scales that look remarkably like hardened feathers, but are composed of flattened hair. i believe the hair is even soft when they are born -- which means that in the life cycle of a single pangolin we can see hair become something like feathers, which become something like scales.