For the unused IO, what I've been told is to just leave the pins unconnected and set internal pullups. You also want to make sure your ground fill a) connects to every point and b) doesn't get too narrow for the amount of current it's carrying. It might not be a bad idea to stick a via or two under each LED considering you've filled the whole bottom layer with ground. In fact, it looks like LEDs 3, 8, 9, and 16 don't actually connect to ground. Did you do a design or electrical rule check in PCB software? Are the Vcc traces for the LEDs thick enough to carry the required current?
Button debouncing can be done easily in software, but 1uf caps work for me. I picked that value mostly because I had about 8 other 1uf caps on the board
That regulator could definitely do with some heatsinking. Since the bottom of your board is empty, what I would do is place a small rectangular fill on the top side of the board connected to the tab, and a bigger one on the bottom. Stitch together with a bunch of vias and you're good.
You should put the bypass caps physically closer to the chip, especially since your traces are so thin. The whole point is to account for inductance in the traces, so you want to keep the traces to the caps as short as you can. You've got plenty of room for it. You're supposed to use a decoupling cap for each pin, but in my current mega328 design, I just used one for pins 4 and 6 since they're so close together.
As for USB ports: http://www.mouser.com/ProductDetail/Molex/105133-0001/?qs=sGAEpiMZZMulM8LPOQ%252bykw6hrf%2fTgEK7uCJf5qM3AwQ%3d Mouser has a few other varieties as well.
Thank you!

I went over the ground connections, and as far as I could see, everything looks all right. To be on the safe side, I took your advice and now there's a via under every LED. I'd done both ERC and DRC, the ERC gives "a couple" of errors, but all of them are of the kind of "Output and supply pins mixed ... ". The problem seems to be my labeling, since all of them mention my net "+5V". My guess is that I've used labels wrong somehow. However, all of the connections looks all right anyway so I assume this won't be a problem in manufacturing.
The VCC traces should be adequate, I used
http://circuitcalculator.com/wordpress/2006/01/31/pcb-trace-width-calculator/ and according to that, 11.8 mil should manage to carry 1A. I've used 24, 16 and 12mil.
I've added 1uF caps to the buttons, with parallell I assumed between +5V and input on the MCU.
I moved the bypass caps much closer. O0
I tried to apply your heatsinking scheme, which sounds like a perfect plan, without success. I cannot get eagle to create a copper polygon connected to +5V. If I create the polygon using rank1, it fills up but won't isolate from ground when connected to +5V, if I change the rank to 2, it won't fill at all. I feel I've tried everything, but I'm new to eagle so I'm probably missing something dead simple. Tried googling a number of terms, but all tutorials on polygon fill seem related to creating a ground plane. Anyone with a suggestion? See attached files polygonproblem.
That USB connector seems to be right, but it will have to wait.
Thank you!

Looking pretty good.
I'd add a bottom ground plane and via stich them well
Hoe about moving the decoupling cap closer to the pins? Generally you wanna route the power trace into the cap the out the other side
Thanks!
I have a bottom ground plane, and now I have plenty of via stiches! Caps positions updated too!