One of the things I do when I play test an instrument is close my eyes and listen as I play the chromatic scale.
I also initially play as lightly as possible on the keywork, this to search for leaks, Even the most minute leak will make an instrument sound just "pretty good" being a far fetch away from 'great". I also do this to test the semi-tones even with alternate fingerings. I don't use a tuner in my final tests but this is probably from being able to tune a piano mostly by ear too.
Some potential identifiers for problems especially with clarinets are:
For example, on a clarinet when you play the low E or mid B press the spatula key lightly. If you press it slighty harder and the tone improves that tells you there is a slight leak on that key or maybe a linked key. It may play perfectly fine but that slight problem can make an instrument drop from a great instrument to a pretty good one.
Many potential problems for clarinets are: the front F (the key under the A throat key) is usually too low to the tonehole. The lower joint top pad is usually too low to the tonehole. And many times the larger "bell" keys are too low thus centering the tone though making it flat too. matter of fact many tonal problems on a clarinet are due to the pads being too close to the toneholes. Many "symphonic" players with lower volume airstreams might not identify the problems but play it with a high airflow and problems start sticking out like sore thumbs.
On saxes this is mostly evident on the low Bb. But as one gains more experience you can test this on nearly every key.
My Selmer mk VII alto is another example of another potential problem. Other than the fact that it's a VII ..
I had played this for years, decades actually before I thought that the tone would drop off over time.
While checking it over I found a very small cut in the palm D pad - this was after over time many repair tech looked over my sax and found nothing and before I started doing tech work. I replaced this pad and wow, the tone did a major improvement over the entire range of the horn. Believe me, people loved the tone of the horn before the "fix" but after it people loved it, even VI players that I knew. This problem also was the reason the pad would take on water and turn dark. The horn played "great" from top to bottom but even better after that one correction.
My initial tenor was a Couf for years. About a decade back I thought I needed a new pro horn so I looked at a bunch and play tested a bunch of horns (Selmer Series II, CB, Yamaha 875, etc). I've found that if you play a bright mpc on them they all kinda sound the same. If you play a dark mpc on them then this brought out the various nuances and differentiated the horns in their tonal characteristics. now keep in mind that of the players I play for they all think I'm the darkest sounding player they've heard. And back then I was able to play a 4 reed on an 8 tip. Of course I relate this to the reasoning of why I have to wear glasses now as the back pressure / head pressure probably popped my eyes out of my head
I don't do that anymore, but the tone was awesome.
But after playing a variety of horns I bought a Cannonball. This also was the time when I was researching / testing / experimenting with the internal characteristics of necks, and the CB neck at that time was roughened up. I noticed too that the hand hammered necks that I had also had "patterns" inside. And the water pressure created ones were smooth. I found that the smoother the neck, for me, the brighter the tone. Of course I also then learned of the various neck tip openings and tested those (all other characteristics NOT being equal) and found the larger the neck opening the more spread the sound. But the sampling size was small and the analysis very limited.
But I degress
In play testing I also found that old pads, say 10 years old seemed to play perfectly fine. For say 10 minutes. Then due to their age and pourousness they would absorb some of the air moisture, expand a bit and a horn that was perfectly sealing 10 minutes ago now leaks like a seave and requires a heavy hand to close all the keys. Of course this may vary from old pad set to old pad set and use but it is something that I keep in mind anytime I play test.
Of course all this knowledge makes me think when I playtest a horn not how the horn itself currently plays but how I can put a setup on it for it to play the way I want it to play. So when I hear someone played a "bad" VI I'm always curious why is it bad - minor leaks which affect response; key corks which are too think which have the pads too close to the toneholes which affect tone and intonation; and a variety of other potential problems I've learned over the years.
But then I started researching what makes a "sweet" horn .... sooner or later I'll start accumulating various bore tapers and tonehole diameters. I've done that for clarinets, but I'm curious for saxes too.
Going back to saxes and playtesting, that CB lasted for about a year with me. I wanted something more and I had to look back at vintage saxes. I got my hands on a closet mk VII. The tone was awesome and BIG and uncontrollable unless you really blew it. But it was a beautiful horn and fantastic tone. This is where I learned about octave vent holes and the various sizes and how it can affect the tone and response. So a horn that I found to be lacking in playability, other than loud, then became very flexible for all genres of playing - I capped the octave vent to make it smaller which allowed proper pressure in the horn. How was this affecting the playability ? I noticed that when the body octave was opened the pressure in the horn dropped. This basically affected the reed. With a hard reed and large tip there was no problem. With a soft reed and small tip the pressure drop allowed the reed to slap against the facing and one would get a squeak. I tested a variety of mpc tip openings and reed strengths and I was able to feel the air pressure drop in my mouth. It was all quite interesting. Many players will say one has to work on their airstream, which when one used a very and high volume concentrated airstream at the moment the body octave opened certainly helped it's playability. But asking a player to play this way just for the "break" is way too much.
But play testing takes alot into account including the player, mouthpiece / reed, neck, design characteristics, and setup. I always now try to keep all that in mind any time I play test any instrument.
And now my main tenor is back to a Couf, where I started.
YMMV