Bikes are excellent value used. You have to know a bit about it to make a good decision, but bikes tend to be super sturdy, and their value goes down after a few years. Bikes are definitely my favorite piece of "gear" to buy used.
Otherwise, I think REI's used section typically has only stuff in good condition. I wouldn't buy a helmet used, but stuff that's meant to last, like packs, tents, some clothes, etc. should be safe
Usually when buying used, if it's something that is for safety such as a helmet or climbing harness I will always buy new. If it's for comfort, like a new pack or a pair of hiking boots, I will at least try on a pair new before I pull the trigger. If it's a sleeping bag, mat, pillow, or an item of clothing which you know will fit, take the leap of faith if says it is in good shape. Psssst, I also like geartrade.com for a lot of used stuff. Don't tell the REI people though.
If we're talking about getting started, I think it takes a while to prioritize what to spend money on - ie, get new.
When I was a teenager in the 1970's we had crappy equipment: uncomfortable and cheap backpacks (World Famous), tents that leaked (usually borrowed), heavy aluminum canoes, and big bulky sleeping bags. Somehow, we were smart enough to get the best boots that were available at the time (though they took considerable breaking in).
Based on that, I would say do what you must to get what you need to be out there. Upgrade when you can.
There's a lot of great gear you can get used. I've got used snowshoes, jackets, rainpants, backpacks, trekking poles, etc. Really most things should be okay, as long as you understand what you're buying and you inspect the item in question. If buying online, there is a 30 day return, so you can always try it, and if it comes and its in poor condition, you can send it back. Personally I find the garage sales are the best as the deals are better and you can see the stuff in-person.
The only things I wouldn't buy used would be saftey equiptment. REI does a good job not reselling this stuff, but I know people who have expressed interest in buying climbing gear or other safety equiptment used through other websites. Things like harnesses, helmets, ice axes, crampons (to a lesser extent), and rope should probably never be purchased used, as these are things that will protect your life and as a result you need to know exactly how they have been treated and what condition they are in so you know when to retire them.
I've purchased most of my beginner backpacking gear from a used gear sale. The reasons people return things can be interesting or downright funny. Here are the big items I've purchased from an REI used gear sale:
Thermarest sleeping pad (reason returned: not long enough)
REI Halo +25 Sleeping bag (reason returned: too warm)
Extra jetboil cup (reason returned: didn't use enough)
Black Diamond poles (reason returned: customer found cumbersome)
Down booties (reason returned: not warm enough)
Patagonia puffy jacket (reason returned: down feathers coming out)
I've had zero issues with anything I've purchased and am happy to a) save money and b) pick up something I normally wouldn't at full price (down booties or the extra jetboil cup)