Use DVD players can be a delight or disappointment. Much of that depends on where you purchased it. Someone selling their old DVD player because they want to get a new one and they want to upgrade to Blu-Ray is probably selling you the DVD player exactly as is. They've used it, possibly for years, and now they simply want to get a different model so they're selling it off. The player could've been abused, the inside could be choked with dust and there could be various problems with it.
That's not to say that when you're buying used DVD players you should never buy from an inpidual. But you should be aware that you're going to get a piece of equipment that you know very little about so you should price it accordingly.
Used DVD Player Sales
On the other hand, used DVD player sales at stores both off-line and online that deal in used merchandise will often have DVD players that have been refurbished and carefully inspected. There's no guarantee there will be, but they are more likely to make sure the equipment is of good quality before they sell it than an inpidual will.
Regardless of where you purchased the player, you want to find out how old it is and how many years it's been in use. Ask if it's been stored for while unused because that could mean it's had something heavy on top of it or that it's been a very dusty area, both of which can damage the player.
Finding the Best Used DVD Players
The best used DVD players are typically the ones that started out as the highest quality players. Generic and bargain players that were cheap to start with typically aren't built to last. By the time they are sold as used players, they may have already met or exceeded their general life expectancy and will break down very quickly.
Rather than purchase one of these, choose a used model that was expensive new and you'll have a much better chance of getting more years out of the player.