What to do with unused analog inputs?
A pull-down resistor is good, yes.  Not only does it stabilize the inputs and prevent any excess current draw, but it has the hidden benefit that you can use them as a Sample and Hold capacitor purge device.  If you read an analogue value from one of these extra inputs in between readings from your other inputs it can make your readings a little more stable as the sample and hold capacitor will be always starting from the same level.

The smaller the resistor the faster the capacitor will discharge, but the higher the outrush current.  Something around 470Ω is good.  Also protects against the pin ever being configured as an output and driven high.