Supply rail caps...
Personally, I wouldnt use 'Audiofile' type caps here....
They are important for IC Protection, as they work in conjunction with the 8 diodes accross the output pins, to prevent 'Overshoot' of the output pin due to the inductive load of the speaker and the series inductor of the Lo pass filter....These chips work at very high frequencies, continuously varying between 100Khz and 1Mhz as I recall, in a near square-wave, so overshoot is a very real issue which can and does destroy chips...Been there, Done that!
They MUST be Low ESR types, Good quality the sort for high temp service in SMPS are pretty cool, Panasonic make a good range of this type......
I would advise Voltage rating of 25V and I would stick to the 'stock' value of 2200uF--No advantage in going smaller here...
Looking at the board layout, the caps are FAR too far away from the supply/earth pins, Tripath recommend in their documentation that they must be placed as close to if not actually on these pins to be properly effective at their job, (Protection, Not Decoupling!)........I would leave the rail-caps as they are, and add a couple of 220uF 25V Lo ESR Directly On The Power to Ground Pins for each output channel...
(This was the problem with this chip and the higher power TA2022 and one reason why its being phased out The pinout is a Swine to work with, and comply with the requirements like this one! I spent some weeks back in 2000, designing round both these chips, and actually advised tripath of this issue, and they sheepishly admitted their mistake, but it was too late at the Production stage....)
Why use such large Polyprop High Volt caps at the Input??
--No point as far as I can see, apart from the sheer size as they would then Look impressive, but I fear they may sound worse than a cheepie lecylytic in this position ...
The Output decoupling caps, are to remove the HF from the wave-form. I experimented with these, and found the 'stock 1uF most suitable. Later designs have used as small as .22uF, especially in the parralleled output 100W set up for the 2020 into 2 Ohms (Output Voltage Offset Servo circuit needed for this...)..
Have you seen the TA2020-020's replacement? The TA2024 I believe, A 25W SM device with the 'die' uppermost and pins on either side. Much better pinout to work around!