From a REST perspective, the URL is 100% irrelevant.
I havent tested it with analytics or anything, I'm pretty sure that the number of people who go "oh, my form failed. I'd better see what the URL is. Oh, /things!' How odd? I expect that to be a list?? What's going on???' is zero.
/things works because it's both the list of things and where you send data to make a new thing in the list. From RFC2616:
The POST method is used to request that the origin server accept the entity enclosed in the request *as a new subordinate of the resource* identified by the Request-URI in the Request-Line.
Emphasis mine. It is arguable that /things/1 is not subordinate to /things/new, and therefore, it's better to POST to /things.