Certainly nothing wrong with buying a used bow as it's a great way to get a year or two old high end model at a significant discount over this year's models. Most manufacturers are going to apply their warranty period to the original owner however there is at least one that has a transferable warranty...sorry I don't remember the name right now but it's one of the mid-size players.
I'm not sure what you'd do about a stolen bow...used purchases online carry all the same risks as buying computers and bikes and everything else. Theoretically it's possible but I've never heard of it happening.
In terms of what to look for: you always want to look for cam damage, cable and string wear (easily replaced), damage to the limbs particularly at the limb pockets and axles, stripping or cross-threading of various component mounting holes on the riser, etc. Lately I've come to view ebay as a little inflated on used prices but the Archery Talk forums are a pretty safe place to buy if you do your research...tons of variety there, they have a black list of questionable sellers, a feedback process, and I have found that nearly everyone provides honest assessments of what's for sale. If you're buying in a shop obviously you have the product in front of you and generally that brick and mortar store wants you walking back in again.
If you're just getting started, definitely take the previous posters advice and visit a couple (or more) shops and shoot a wide variety of bows...short, long, slow, fast. A good shop will spend a lot of time with you, make you feel comfortable, explain things, answer questions, etc. In the end, don't get too hung up on brands and buy the bow that feels best to you. We're fortunate to live in a world where all of the major manufacturers are producing superior hunting tools. Don't shy away from ready-to-shoot packages but be prepared to upgrade sight and rest.
Two years ago I was where you are at now. I found a shop that made me feel comfortable and they probably spent 2 hrs with me my first day in the shop. I found a bow I liked and walked out with it. But be careful...I've walked out with two more since then ;-)