An accordion can look new, or particularly in the case of cheap Chinese accordions, even be new, and still have problems.
An accordion needs to be tuned or serviced every decade or so, the more it is played or abused, the more often. Most accordions in America have never been properly serviced. If the accordion is more than 15 or 20 years old, and has any problems, it might, or might not, need a complete overhaul of the reeds!! That is, if any of the accordion notes don't sound 100% right, to fix them may or might not require all the reeds to be serviced. The older the accordion, the less likely a remedial tuning job will be effective, as opposed to a complete reed "overhaul". The reeds in over 99% of all accordions are glued in place with a mixture of beeswax and rosin. This deteriorates over time. One reason wax is used instead of a more permanent material, is that it can make it easy to replace a broken reed. By the time the wax goes bad, when the accordion is played regularly, the reeds will surely need cleaning and tuning anyway. Special accordion wax has the useful property of absolutely sealing against air leaks while tightly gripping the reeds to efficiently transmit tone vibrations to the wood parts of the accordion, and also it can easily be melted at a low temperature.
The "average" or median accordion, a 3/5 120 bass 41 key piano accordion, with 3 sets of treble reeds and 5 sets of bass reeds has 41 X 3 + 5 X 12 = 183 reed plates with a reed on each side = 366 reeds. This compares with the number of strings in a piano, except when a reed is tuned, it is permanently altered, sometimes weakened. If the wax is really old and bad, the accordion has probably never been tuned and to fix some of the reeds means all the wax has to be poured new, because when you take out one reed, the wax breaks up around the other reeds, and pieces of brittle wax can get on the reeds and choke them or soil them making the others go out of tune. Sometimes the wax is not so bad, and a few reeds can be tuned without pouring new wax. A complete reed overhaul of your accordion, including cleaning, anti-rust treating, tuning, pouring new wax, straightening or replacing reed valves, and minor repairs, can take 20 to 40 hours of work. Most of accordion the reeds have a one-way valve attached to keep them from wasting air when the accordion bellows are squeezed or alternately pulled. If the accordion was stored in a flat position a good while instead of vertically half of those valves (usually leather) will sag and cause the notes to sound bad. When the bent leather is sucked over the reed slot the reed will "sizzle" or "sniffle" or else snap suddenly down as pressure increases. If that reed valve doesn't close at all the note will be sharp out of tune, and feel "windy". Note: sometimes the reed valve is "film" or plastic, which will seldom curl, but can also have problems. Hohner Accordions since the 1950's have this kind, and they are now preferred by nmany manufacturers. I use them a lot because they don't curl and are uniform in quality.

Never buy an accordion that smells damp!!

Appraisals

It is nearly impossible to determine the real value of a used accordion without having a good player test it. The monetary value is primarily a function of the "rental" value, or how much money can a good player make per hour playing it. The better the accordion, and the better the player who plays it, the more value it has. That is why I don't and can't do appraisals through the internet.

Testing

Rule #1. never but an accordion that has any problem, unless you know how to fix it.

1. Listen for leaks, usually a hissing or breathing sound or a note that constantly plays even when the accordion has no keys or buttons pressed and the bellows are moving.
2. Play every key and note with the bellows moving both ways, and if the accordion has switches, repeat that process for every treble and/or bass switch setting. Check for any notes that sound bad.
3. Look at the straps to see if worn or missing and the condition of the carrying case, if any.
4. The condition of the bellows: If worn, it usually indicates the accordion was used a lot without having been serviced much. If it was used a lot, that may be a sign that it was fun to play, but worn out now. In addition to numerous repairs it probably needs, a new bellows if needed, starts at about $300 and has to be custom made in Italy. There are no longer any dependable economical specialist bellows makers in the U.S.
5. Smell the accordion. If it smells nice, it is more likely to be repairable with a reasonable amount of effort (but don't assume that). A moldy accordion will surely cost more to fix than the end product is worth, at least monetarily.
6. Look to see if any screws or pins are missing, and for any broken hardware on the outside.
7. Check all the keys and buttons for evenness, rapid action, and equal spring pressure. If the treble keys are all too high, or set at an uneven height, the accordion will be hard to play. If some of the keys are way light to the touch, they may not stop the sound when the accordion is squeezed. The buttons can get stuck down and cause a chord or note to sound all the time. Push each of the bass buttons at least 1/8 inch (4mm) below the panel, but be aware that sometimes the buttons won't go all the way down due to design quirks. The ones that will go down that far should not get stuck there. However if the accordion is in a flat horizontal position, especially, if several chord buttons are depressed at the same time they will all go down. That is normal. In a perfectly functioning bass macine, they should all spring up promptly if the accordion is vertical. In an 120 bass accordion, there are only 12 springs holding up 80 buttons in a the chord section, so that if several chords are pressed, all the 12 valve springs of the chromatic scale holding up all the chord buttons will take away all the spring pressure on the 80 chord buttons. (The other 40 are bass notes, in 2 rows next to the bellows). If the accordion is thrown during shipment, as UPS always does, all the bass chord buttons may collapse due to a few being stuck. Often if you take off the bass panel, you can just tease all the buttons back into place and they will work again.
8. There are things you can see on the inside of the air chamber if you know how to unfasten the bellows. Usually there are six, seven , or eight pins to pull out to take the bellows loose and look inside. If you went to that much trouble you probably already own it, or trying to prove something.

9. An accordion that has any malfunction should not command a high price due to the possible cost of repair and the problem of finding a good repair person.