What should I look out for when buying second-hand aquarium equipment?
In a word, reliability. Typically aquariums, heaters and filters are fairly crucial in keeping fish alive and their failure can be disastrous. Firstly you should ask yourself whether the savings on such key items are really worthwhile, then place higher currency on trusted manufacturers.
It's unlikely that equipment will carry disease if dry and clean but it's not unknown for second-hand set-ups to come complete with undesirable residents in the shape of aggressive or hard-to-rehome animals. Remember that retailers might not welcome the cast-offs, so expect to keep any inhabitants that come with bargain tanks.
Silicon aquarium seals are normally good for at least ten years, possibly a little less for black-coloured versions. Check for obvious damage, cracks etc. and remember that moving glass tanks with substrate or water in can lead to breakage. When transferring a mature tank, take care to treat the filters with the same care as the fish, as cleaning them out can lead to fatal crashes in water quality.