If you’re using TouchID and having issues, you might have less of them under the 7.1.1 update. Redditor iOSecure (via iMore) posted some insight into the Touch ID process, and the improvements made under 7.1.1. He points out that while TouchID is supposed to improve over time, if the scans aren’t great to start with, they don’t really get better.
From his post:
With iOS 7.1.1 Apple now takes multiple scans of each position you place finger at setup instead of a single one and uses algorithms to predict potential errors that could arise in the future. Touch ID was supposed to gradually improve accuracy with every scan but the problem was if you didn't scan well on setup it would ruin your experience until you re-setup your finger.
iOS 7.1.1 not only removes that problem and increases accuracy but also greatly reduces the calculations your iPhone 5S had to make while unlocking the device which means you should get a much faster unlock time.
So under the latest update to iOS, the initial scanning is improved, and the unlock is more efficient, so it should work better, and also faster. Both of which are fine improvements.
Other reports have claimed improved battery life and a decrease in spontaneous seboots, so if you haven’t updated yet, now is an excellent time to do so. Have a backup first, then install it. Better safe than sorry and all of that!