There are a few things including overall condition, control functionality and service history.
It might sound obvious, but the physical condition of a piece of gear tells us a lot about how it’s been looked after. Gear that has been well-cared-for is almost always a better bet than gear that’s been neglected, other things being equal.
This extends to service history. All equipment needs periodic maintenance and parts replacement. Can the seller show you any records or invoices for past work? Has this work been done by a reputable technician? Older gear can need extensive maintenance. Don’t let this put you off, it’s still often much better value than buying new, but the work HAS to be done.
Performance – I suggest almost never buying something you can’t see and hear running. Anyone who says they can’t show you something running should be avoided – like the plague. Are you going to just take the word of a random seller that the equipment works well..? I wouldn’t.
Does the equipment turn on and run smoothly? Does it sound good? Do all the controls and switches work as they should? These are all things that can be checked prior to purchase. How about a warranty? If buying from a business, there will be some kind of warranty against defects. This can be very helpful. Some non-business sellers will offer returns if there are problems but this is rare.
Hi-fi equipment purchases should be made with a cool head. It might be rare and collectible, but if it’s broken, it might also be the world’s most expensive doorstop, and we don’t want that!