I still get failures but it's a software issue. I know this because it fails with every registered finger. Here's a few things I have done to improve until Apple fixes it.
1) Register most used fingers like right thumb twice. To keep up with which one be sure to rename each scan/finger after you finish each one such as Right Thumb1 and Right Thumb2. Scan 1 beginning with fat/flat part of thumb and #2 start with tip of thumb. Obviously you only have 5 slots available but it helped me to store two scans of my right thumb.
2) even if you do #1 it will fail and when it does the only fix is to login with you passcode and it will recover on next lock.
3) I have also gotten more success when I press the home button is to maintain contact with the home button to let scan finish. Being a longtime iPhone user with passcode, I would press the home button, then lift my thumb then lay my thumb back on the button to let it scan. For some reason this seems to confuse the scan process causing more failures and it to bug out and go into full failure mode requiring passcode to recover. This is what's leading me to believe its software based and eventually fixable by Apple.
It's so nice not having to slide/swipe your finger to make it work like previous generations of print scanners. Granted, the technology will improve which means that there will be limitations in this first iteration (iPhone 5s) and those that will be disappointed with nothing less than perfection but that will always be the case. Apple will improve some of the early issues but some will remain and won't be refined until the next hardware version, i.e. iPhone 6. We can hope though.