How to determine wattages on an applications note schematic?
Average (only slightly pathological) worst-case (20W average power out into 8 ohms at 20kHz continuous sine wave) power dissipation in the 4.7 ohm resistors will be around 120mW. 



Edit: In case you're curious how I got this whilst avoiding any math mistakes, well it's Saturday, and I'm lazy, and calculations look a bit too much like what I do for paid work, so I just simulated it in SPICE. Of course I could do it manually or in Matlab etc. too, but this was easy. 



The W markers are like probes that measure the instantaneous power dissipated in the components. The 17.888 peak voltage was picked to give 20W out (and verified by the marker): 

VAMPL = \$ \sqrt{2} \times \sqrt{20W \times 8\Omega} = \sqrt{320} \$ V. 



Real dissipation playing any sensible signal source for listening will be a lot less. 

You can use 1/4W for everything resistor-wise. 35V rating is okay for the capacitors since you should never get close to that for the supply (and they usually have a surge rating that allows you to slightly exceed the rating), but I'd use 50V and 105°C for some margin.

As a check - look at the parts on the sample PCB layout. If the resistors are not physically large, they're not high-power. 

That doesn't mean that if you did something really perverted like feeding a 100kHz sine wave into the input (and cranking it up so you got 20W out despite the roll-off of the amplifier) you couldn't muck up those resistors by making them dissipate several watts. If you're nervous, 1W resistors are cheap and not that huge.  

If you want to read more about the series RC on the outputs, they're called Zobel networks or Boucherot cells.