FWIW, I think there are several different issues here:
1. Some people (I suspect very few overall) may have defecive hardware. For example if you cannot even register your prints then that suggests the hardware is defective and you need a replacement.
2. Some people are not registering their prints optimally. Things improved hugely for me when I changed the way I registered my prints as per advice on this forum and elsewhere.
3. Some people may not be ensuring they are making good contact with the metal ring around the home button when registering or, more likely, when unlocking. Good contact on the metal ring is essential.
4. The 7.0.3 update seems to have improved things considerably for many folk, for unknown reasons.
But having said all that, some people are still having issues. In my case things are pretty okay now but I do still see a degradation of recognition of the print I use most often to unlock. Interestingly i do not see a degradation in the other prints I have registered but which I hardly ever use. This leads me to consider a 5th factor:
Apple have stated in a few places that 'TouchID gets better the more you use it'. This suggests to me that it incldues some 'learning' algorithms that dynamically modify recognition as you use it more and more. I suspect that there is some flaw in this algorithm such that for some subset of users (myself included) rather than getting better with more use it actually gets worse. This would explain my experience where:
a) Prints that work perfectly across a wide range of angles/parts of the fingr tip immediately after registering become much less reliable over time (assuming they are being used a lot).
b) Prints that work fine after registering but which are then barely used continue to work just fine. Presumably if they were used a lot they too would degrade.
If this theory, and it is just a theory, is correct then this is a software issue and it is very likely that Apple will address it in an upcoming update. Especially if we all leave feedback regarding this issue.
I have to say that though I do still see some degradation in recognition reliability for my main print (right thumb) over time, TouchID is still very usable for me and I find it a great convenience. Even with this issue it is still far more reliable for me than any other fingerprint recognition technology I have used in the past and it is a safe bet that it will only get better as Apple refines it.