My Rant
But is it a rant?
Look, first thing is first. Adding Touch ID is great. It's another option of convenience for those that can and will use it. With that said, here's what you should consider.
Touch ID allows for 5 prints to be stored. Maybe 3 of yours, 1 for your wife and 1 for your kid.
I'm eager to learn how Touch ID responds to a paper cut or a splinter. If you stored only 1 print and relied on that finger, it would suck to be locked out of your own phone because you got a splinter. Always have a back up print. To deal with this, one would think that Touch ID and Passcode could be used simultaneously. I would love to set up a complex pass-phrase on my phone, but I don't currently because I don't want to re-enter it 15 times a day. If I could short-cut that complex pass-phrase most of the time with Touch ID, great! Now we're getting somewhere.
Additionally, if something happens to your fingers, such as grabbing hot metal for no good reason, and you burn the skin off, you have a recourse to access your device.
So, let's move on...
You've set your kid up to use your device. Each print should have permissions. I would want my kid to be able to unlock my device, but not buy apps on the app store. Additionally, to address the police concerns raised previously (and I originally thought of this too) I would want one of my prints to lock down the device and Touch ID. Doing this would then require my complex pass-phrase or pass-phrase/Touch ID combo.
However, if Touch ID replaces pass-phrase and passcode when used, then it is as simple as being restrained while someone scans in your print.
To give Apple some props though, I'm glad the prints are only ever stored in the device and never transferred out. That there's actual physical security in the chip to protect the data from becoming compromised. Great job!