And short of doing nondestructive testing, you won't know if it (metal gear like carabiners, etc) is truly safe.
Destructive testing has repeatedly shown that used hardware is generally safe. Unless the hardware was visibly damaged, it held up as expected. The whole "micro-fracture" and "aluminum fatigue" myths have been debunked many times over.
Black Diamond says "If only light scratching is visible and gate action is still good, there is a good chance it is fit for usage." http://blackdiamondequipment.com/en_US/faqs.html#CLIMB
Sure, it's possible the carabiner was in a fire that wasn't hot enough to melt, or dunked in industrial acid that somehow didn't effect the electroplating... but what are the chances? You're much more likely to die rappelling off the end of the rope than a carabiner failling. Failures of carabiners in good shape are practically unheard of.
General advice is to avoid soft goods like runners and harnesses since there could be damage you can't see, or as a beginner not notice.
Don't buy a used rope since you can't see damage to the core. That said, I have no problem buying and selling any of this stuff among my friends... chances are I'm climbing with it at one point or another so no big deal.
Mixed gear like cams w/ slings... if the metal is undamaged and the action is smooth, it's probably fine, just have the sling replaced. Ditto with slung hexes and stoppers.
Helmet; depends on the type of helmet. A hard shell should be fine if there are no cracks nor visible damage. Foam helmets, you can see all the foam so it's easy to see if there's damage. A hybrid is more difficult since you can't inspect the foam core... probably better to avoid those.
As for backpacking gear... shoes/boots with less than 25 miles are usually fine. Tent, pack, no problem with those. Sleeping bags, pillows, base layers... you should be able to clean and defunk them... but they are rather intimate and if you're really sensitive to that kind of thing, you might want to buy new. If you're really sensitive to cigarette smoke or recently quit, seems like you can still smell it even after you've washed the item several times.