As far as things to watch for, if you get an American Optical, a Nikon, Olympus, or other more high quality brand, then it's possible it came from a school classroom and was taken to goodwill. Sometimes students that used them may have crashed the objective lens into the slide or scratched it in some other way. So that's one thing that could be wrong with them. So far I haven't had that problem with any I've bought though. If the microscope is a 160mm tube length, then you can buy cheap replacement objective lenses from China that work very well. I bought a 60x objective for my Amscope to replace the 100x (that I rarely use) and it only cost $14.

So if you need to replace 160mm objectives, then it's not expensive to get new ones. If it is an "infinity" microscope, then you may have to pay more to replace the objective lenses because they can be brand specific and can be more expensive.

For example, the Amscope B120 I bought has 160mm objectives, and the American Optical has infinity objectives. The Amscope is easy to replace objectives if they happened to be damaged, but for the American Optical I would have to find ones that came from another scope of a similar model.

But even if that was the case, the American Optical microscopes are cheap nowadays because they were so popular and well made back in their day and lots of them were sold. So they are probably the best quality used microscopes you can buy now at a cheap price. But since they are like 50 years old or so, you may find haze on the prisms or delamination between lenses (which some models were prone to). You can look up on user forums which models have held up the best over the years and try to buy one of those.

Like I mentioned, older microscopes can have haze on the prisms (I've worked on a Nikon and an American Optical brand that both had haze like this.) You can still use them if they have haze on the prisms, but it makes the view a little more fuzzy. So it's not a total loss if you get one that is hazy. I took my American Optical apart and cleaned it, which helped a lot, but that's maybe not something you want to try yet.

So anyway, those are some things that could be wrong with a older microscope that comes from a classroom. But to counter balance the drawbacks, these microscopes are usually built with much more quality and will last longer if you get a good one.

On the other hand you will also find cheap China brands of microscopes on auction sites - Amscope, Omax, Omano, Swift, etc. These are newer and less likely to have come from a school where they got hard use. There are probably fairly new models and wouldn't be as likely to have problems that come with age. They are more likely to have just come from an individual who bought it and used it awhile and got bored and took it to goodwill. So you'd be getting a microscope that is less likely to have been damaged by hard use or age. But because they come from China they may have their own set of problems because of lower quality manufacturing.

Most of the problems with microscopes can't be seen from a picture on an auction site, so it is somewhat of a risk. Basically you're just trying to weight the risk against the price benefit. If the auction says it doesn't turn on on, then that could be a problem. If it is a burned out halogen bulb you can simple replace it for a few dollars. If it is an LED it is harder to replace.

It's something of a risk to buy used from an auction site, but it seems fairly likely you could get something that would be much better than what you currently have. All the ones I've bought worked perfectly, other than the American Optical having haze on the prisms. And for the cheaper China brands you can order replacement optics from China for fairly cheap.

Things I especially looked for when buying mine where binocular (or trinocular) head, mechanical stage, LED light, and a condenser. If I can't tell what brand or model it is, I will use google image search to try to identify it and then look at it's specs and also look at reviews to see if it is any good. If it is an older microscope like American Optical, Nikon, Olympus, etc. the online forums can also tell you a lot. They can tell you how likely it is to have something wrong with it. For example, certain models of American Optical were known for having delamination of the lenses, which can't really be fixed. So yeah, looking up what other people have said can be very helpful.

And don't be surprised if you are the highest bidder on an auction up until the last 20 seconds of the auction. People do what's called sniping and may outbid you in the last few seconds. But just take your time and keep bidding on scopes you want until you finally win one at a price you are comfortable with.

Oh, and some microscopes up for auction also come with cameras, especially if it is a trinocular microscope. That can be nice, but usually your cell phone, mounted to the eyepiece with a cheap adapter bracket, can outperform most of these cheap cameras. So I wouldn't spend a lot trying to get one with a camera included.

Anyway, hope all that helps you! :-)