The only buttons on the 720 that make the "clicking" sound are the silver ones.
These are the directional/OK grouping right above the Transport buttons -- left arrow, right arrow, up arrow, down arrow and "OK" in the center of those.
Also the silver buttons surrounding the directional/OK buttons: Volume up and down, and Channel up and down
Also the three selection buttons on either side of the color LCD.
And the large Activity button at the very top.
Sounds like a lot, but it doesn't seem that way when using the remote.
I had to go back to the remote to check on this -- the only ones I remembered clicking (and being annoying) were the directional/OK buttons. Turns out all the silver buttons click, but the others had never bothered me. Probably because I use the directional/OK buttons much more.
Anyway, to recap -- the silver buttons click, the others don't.