Should I keep this wine refrigerator?

Most importantly, does it work? The dent on the back doesn't look like it harmed anything, and it's on the back, no biggy. The dent on the front is pretty ugly, but as long as it is not effecting the sealing of the door, it can probably be over looked depending on where you plan on storing the wine fridge. If you are, or know someone handy, the dent might even be easily hammered out.

Lastly, as for the drip tray, go to the manufacturers website and order a replacement one. It looks very easy to replace. It will probably be cheaper than trying to go through the hassle of shipping the fridge back and trying to get your money back. Unless you were shipped a beat up wine fridge to begin with, there is a good chance it was just badly packaged and beat up during shipping, which is very common. Personally, I'd keep it and just fix the small things as long as it actually works. And it doesn't look like a safety hazard.

EDIT: Well, I did some looking around just to see if I could find you a parts link. Couldn't find one. However I did find a lots and lots of really bad reviews on this wine fridge in general. Apparently the fans quit working and it stops working after a week to a couple months. So if yours works, you can either keep it and just hope it doesn't stop working anytime soon, or just send it back and see if you can get a refund. Might not work if the ebay page you bought it from said, "no returns" or "as is". Either way, its your call, good luck. If you do decide to go for another one, I'd recommend a different brand, and do a little research on what other people have said on the product.