In the above thread, you asked how one goes about testing the pedals of a presumably used grand. I can help you here; the same ideas hold true for inspecting the trapwork (pedal mechanism) of a new grand piano. Obviously one should be wary of a new or used piano whose pedals feel loose, or squeak (Kawai grands are especially prone to pedal squeaking), or in the case of grands, the pedal lyre is loose and damaged -- moves along with the pedals.
Rightmost pedal (for both grands and uprights):
As you depress the sustain pedal, watch the way the dampers are lifted. Check that they all come up at the same time, that they rise evenly in height from damper to damper. When you release the pedal, check to make sure that some dampers do not remain stuck in the up position, or that some are crooked and are contacting their neighbors.
Listen for groans when you raise the dampers, and listen for thuds when you release the dampers with the sustain pedal. If you have a competent technician at your side, determine whether the problem can be fixed with reasonable cost.
Leftmost pedal (the soft pedal also called the una corda pedal on grands):
On grand pianos, depressing the leftmost pedal shifts the entire action slightly towards the right, causing the hammers to contact only two of the three strings in the treble section of the piano. Check to see whether the pedal operates smoothly, and that the action traverses with an even feel to it. Be wary if either the action binds whilst moving towards the right. And also be wary if the action does not return to its leftmost position upon releasing the U.C. pedal. There is a piece of heat treated metal located inside the right side of the case, adjacent to the action, that pushes the action leftward when the pedal is released.
While test-playing the grand piano using the una corda pedal, ask yourself whether there is a pleasant, musically desirable change in timbre to the sound. If the hammers are worn out, they are probably way too hard, and have such heavy impact-grooves worn into them, that depressing the soft pedal will align the hammers over the strings where the previous grooves were. The upshot is that you might find a very uneven sound that is difficult to control whilst playing softly with the una corda pedal.
The soft pedal of upright pianos is hardly functional at all in my opinion, and only limit the amount of distance the hammers can travel before impacting the strings. There is no change in timbre on upright pianos -- usually on used grands, the hammers are so smashed down, and hard (from total lack of maintenance by the former owner(s) ) that the soft pedal is essentially useless on only but the finest upright pianos (is that an oxymoron?). Restated: hard, smashed-down felt hammers that were never maintained in decades -- contribute to make the piano sound loud and bright, Soft pedals on uprights can not compensate for this lack of maintenance.
To test the operation of the middle pedal on a GOOD grand piano, first hold down the RIGHTMOST PEDAL (to simultaneously raise all of the dampers), then depress the MIDDLE pedal while the dampers are raised, then release the rightmost pedal. There is a mechanism called a "monkey bar" that slips behind only those dampers that are raised prior to depressing the middle pedal.
We are looking to see if the mechanism will hold up each damper. In normal playing, you hit the note you wish to sustain, THEN depress the middle pedal -- ONLY the damper(s) that correspond to the desired held note(s) should remain raised. The trick with using the rightmost pedal is a fast way to check out all of the dampers at once.
On cheaper grand pianos, the middle pedal simultaneously raises all of the lowest strings' dampers for a pseudo sustained effect. This feature costs less to manufacture, and is one of the reasons many so-called baby grand pianos will not satisfy intermediate and high level pianists for very long.
On upright pianos, some have the same cheating system as described for the low end of grands. It is worthless in my opinion. Interestingly, some mass market upright pianos (Yamaha comes to mind) have a piece of felt that gets inserted between the hammers and the strings when you depress the middle pedal. This is sometimes marketed as a practice mode.
The truth about the middle pedal on upright pianos is this: most piano customers outside of Japan believe that a good quality piano must have three pedals instead of only two --EVEN if the third pedal serves no useful function whatsoever. There is a "more is better" attitude about that pedal; as a result, the manufacturers give the unknowing customers what they "think" they want.
Hopefully you have found this information to be helpful.