"Provide a solder pad". Of course you will. All the IC's pins should be soldered. Always. Leaving it floating is NOT a good idea. It may change level all the time, which may have undesired effects to the internally connected circuitry. You always want to have predictive behavior. If the input has an internal pull-up resistor this is a good solution, though, as long as you don't forget to enable it.
"Connect the pin to ground". That's a good solution, provided that you can guarantee that the pin will never become an output. Output high and you short-circuit the power supply. A resistor would prevent that, but that's an extra cost. Don't use a capacitor; it would leave the pin floating, and the microcontroller doesn't like the capacitive load in case it would become output.
"Connect the pin to a supply source". Same as above: if the pin should become output low you'll have a short-circuit.
"Leave unconnected, but make the pin output". That's the best solution. Don't use the possible alternate functions, like ADC or serial. A high level is preferred in case you forgot to switch off the internal pull-up resistors, which otherwise would cause a (small) leakage current.
For opamps the output can be left open, and the inputs to a fixed voltage, but not both to the same! I recently saw in a Linear Technology application note how they connected the non-inverting input to V+, the inverting input to V-. Szymon rightly points out that this can't be used if the inputs have clamping diodes.
The best thing to do with a surplus op-amp it is to use it. There are lots of places in an analog circuit where a buffer amplifier may improve performance - and a unity gain buffer uses no extra components. (from this article, linked to by Szymon)
Let me start by "Small chip die has specifications X and large die from same company has better specifications" is not an argument for any manufacturer. Of course the larger, more expensive die will have better stuff in many dimensions.
But, are you using bipolar or single ended channels? The page you are looking on is the limitation for bipolar channels, possibly due to some internal stage.
Two pages higher, it says for single ended channels "Aref External = 2.0V to AVcc".
Whether an internal reference track has a certain option is also not a valid argument, as you do not know all the paths internally on the chip itself. So you cannot just say "If I have it switch over internally it can do this, but externally it can't, that's bullshit, I will just do it externally", because internally it may also switch over some stages, that work better, but need to be hard-related to VCC to be able to do that. It may not be likely, but it is possible.
So if you do try it with bipolar channels and nowhere else you can find a limitation to their use that also implies a lower Vref and this is something you want to produce more than one of, then you should still at least test it to further limits than it will ever go in the real world.
For example if you make it for -20deg C to +50 deg C, it needs to be verified to work correctly for extended periods of -25deg C to +60 deg C. As such also with main incoming supply voltage. If the board is designed for 11V to 13V, it needs testing for 10V to 15V, or some such. And not just for a minute, but at the very, very least for the better part of a day at each extreme and possibly several points in between.
And for proper testing, you should test each parameter with each possible setting for each other parameter. I.e. 10V to 15V in 1V or 0.5V increments, half a day each at every temperature between -25 and +60 at 5 degree increments, in the example above.
And that needs to be done with several randomly picked items from each production run.
EDIT:
Doing tests like that with slightly less rigour would be wise, even if you stay inside the datasheet's parameters for all parts. But then you can probably stick to "Test all voltages for a couple of minutes at a temperature below zero, one above room temp and at room temp". Unless it is a very critical part, of course.
Best Answer
First, read the data sheet and the application notes. Carefully.
Generally any unused outputs can stay unconnected. If an apparently unused output needs to stay connected to some source of bias for proper operation of the rest of the chip, then the data sheet will tell you.
Generally all digital inputs need to be connected to a valid logic level to avoid excess supply current, even if you won't be using the function it's driving. If an input has an internal circuit to hold it at a valid level, then the data sheet will tell you that it can be left open.
Generally any unused analogue inputs should be kept within their valid voltage range, and quiet. Study the data sheet for each input to see what the valid range is, whether it will stay within that if left unconnected, and whether power consumption is dependent on its voltage. Ground is often OK.
In professional equipment, unused inputs are often taken to specific voltages through a series resistor. This allows the input to be probed during test, which allows standard test programs to be used. This is not usually an issue for hobby designers.