Recently, we noticed that, for some reason, when an iPhone 6 was plugged into its charger, the Touch ID scanner would not work. So, we did a bit of research, and found out that others reported experiencing the same issue, even with other models, including the iPhone 5s, the first iPhone to feature the scanner.
At first, we thought at first that the cause of this glitch might be a bug in the latest version of iOS (9.1). Instead, the common denominator in each of the cases we read about, which dated back at least as far as early last year, was that the iPhones in question, including ours, were in cases. Apparently, when the iPhone is plugged in, using the Touch ID scanner requires that the user provide grounding by making physical contact with the phone's metal casing.
We tested this, and, sure enough -- as soon as we took the phone out of its case, held it in hand, and tried to use Touch ID, it worked!
As far as bugs go, this one isn't disastrous (thankfully, there aren't really any security implications), but it might be annoying if you need to access Touch ID while the phone is both plugged in and in its case.