Great question, Lyn! It's something I've been wondering about, too, with the influx of designer "inspired" lines at discount stores, the "designer" bags and shoes in consignment stores, and the whole "fast fashion" industry that promises me a runway look for only pennies.
My best attempt at answering this question would be to take a long, hard look at the item itself. Does the aesthetic of the item look harmonious--or are design elements thrown together just to riff off a current "look"? For example, the colours in Target's Missoni look-alikes always seemed to be quite harsh and jarring, totally unlike the spirited, bright look of a real Missoni. I'd also look for evidence of attention to quality--a fabric that skims and drapes nicely on the body in a DVF knockoff, for example, or careful pleating and even stitching on the the dress you've shown.
I guess I'm thinking that an "inspired by" item would give a nod to the designer but still stand on its own merits as a beautiful piece of clothing. A "knock off" relies pretty much just on its association with the designer's brand or image for its appeal to a potential customer.