Aside from the strangeness of going to see a movie based on what it didn't have in it (How often has that happened before? "Come on in and see the circus! No elephants! No strong man! Definitely no clowns!") I think the best indicator that it worked was the fact that most of the time I didn't even notice what had been cut until much later. "Oh wait, wasn't there a gratuitous warg chase they got rid of around here?" "I remember now, they cut the pointless standoff with the elves in that last part," and of course "Richard Armitage looks much better when he isn't having to play Thorin as a brooding hero on a romance novel cover." There was a noticeable drop in film quality when the material from the third movie started, and of course he had no DVD extras to work with on that one, but I imagine that time and the DVD release will take care of that.
-- Peter Jackson, or his set design team, really like those wide open conference spaces. In the Lonely Mountain, in the wood-elves' hall, even in the goblins' cave -- the rulers are always sitting on a raised, difficult-to-access platform in a great hall the size of Grand Central Station. You can see the advantages; you're visible everywhere and there's little chance of a hole-in-corner assassination when you're perched on high for all to see (and hear). Of course, defending yourself against a hostile archer might be difficult. And it did mean that goblins' cave needed to be implausibly well-lit.
-- The acting is good, really good. It was possible to see that in the theatrical releases but the endless "Cue chase scene!" bits made it very easy to lose track of that fact and/or start getting distracted by counting the number of times when a dwarf is either hammered by some gigantic foe or falls from a ridiculous height and still manages to emerge without so much as a fractured ankle. There's certainly a lot of material in the appendices, but I refuse to believe that Tolkien included any footnotes about how dwarves and hobbits have titanium skeletons.
-- Cutting 90% of the fighting scenes made the remaining ones much more effective. When Thorin and Company arrived at the entrance to the goblin caves and began bunking down for the night, there was actual perceptible tension there. Before this their only real hostile encounter had been with the trolls, of whom there were only three (and not the brightest three specimens either). When Bilbo kills the spider in Mirkwood, it's the first time he's done anything really physically courageous. It stands out as an important moment, just like in the book, as opposed to fading into the background as it does in the movie.
-- The pacing in the edit was very, very quick -- sometimes too quick, since the dwarves were doing things like desperately shooting at the stag in Mirkwood seemingly about five seconds after entering. Part of this was probably just lack of material to replace the cut bits with, but considering how fast the book moves I don't think it was that bad a problem. There were a few continuity issues -- we see Bilbo wearing his mithril shirt and never find out how he got it -- but again, nothing fatal.
-- I was amused to see that the sole remaining scene featuring Alfrid (the wannabe-Wormtongue) was the one where he fawns over Bard and tries to proclaim him king. Since the only other glimpse of Alfrid that we get is a brief moment where we see him at the Master's window, looking surly, in this edit it's perfectly plausible that he's sincere.
-- The drench-Smaug-in-gold scene was partially retained, probably because there was almost no way to avoid it entirely while still keeping most of Smaug's dialogue. However, the buildup to it is almost entirely gone; the dwarves manage to rig it up in about thirty-five seconds during their first encounter with Smaug, which at least makes them look uncharacteristically competent for a brief moment. Ordinarily I would complain about this but since it was such an unnecessary scene in the first place I can't really bring myself to do it. (Especially, as A. pointed out, because the CGI for the molten-gold effects was so terrible -- I think he was experiencing actual physical pain when we saw it in the theater).
-- It was very nice to see Legolas again -- for three seconds, closing a door and walking into the Wood-elves' hall. It was a perfect cameo, a restrained nod to the LOTR movies. Which, in the end, is what The Hobbit should be as well.