The quality is good, although not without a few of the standard Land Rover niggles.
My 2003 Discovery's build quality was very good, IMO. It was a very solid vehicle that I had only a few problems with in the ~30k miles I drove it. Just the standard Rover stuff, and a few breakages: power steering pump died, rear wiper fell off, transfer case got very noisy and was replaced, and after the first oilchange it leaked oil like a seive until the metal piece the oil filter sat on was replaced. Sounds like a bad list but really the truck was solid.
After nearly 10k miles in the LR3 I can say that the material quality is much better, and the truck is loads better to drive... And build quality is better, but still not Honda great. I had to have a door seal replaced (poorly seated from the factory), I have an odd power steering noise when backing out of a parking spot and turning the wheel that the dealer "can't replicate" and I occasionally get a drip of water on my foot (but the "drains are clear"). Also, the auto wipers sometimes have a mind of their own. Just stuff I laugh at and say "well, it's a Land Rover."
Interestingly enough, we just experienced our first issue with my wife's year-old VW Bug Convertible. The turbo wastegate sounds like it's not opening properly. I realized I've never had that car in for an unscheduled maintenance... Like I'm so used to with Land Rovers.
So Land Rover is getting better, but they're still not "there" yet IMO.
FWIW--I am getting remarkable mileage in my LR3. I average 16-17mpg in the same loop I got about 11.5-12.5 with in my 2003 Disco. I have gotten as high as 20 on the highway, I got 17 fully loaded (and I mean FULLY) with 4 people and a rooftop Thule backpack at 80mph last week. Lowest ever was about 14, which was all city. My lowest ever in the Disco (all city) was about 10. So I'm really happy with the mileage.
The engine has really loosened up lately (seemingly around 8k miles or so) and it really hauls now. I really love the engine and the handling. I forgot how slow and ponderous the Disco 2's were until I got one as a loaner a few weeks ago... I was surprised to find how much faster I'm used to driving the LR3 on the road.
The tires, OTOH, are Goodyear Wrangler HPs. Sh|ttiest tires known to man. Goodyear redesigned the HP for the LR3 and still f*cked it all up. They are mud tire loud after 10k miles...
And no mud tires available yet. PITA. That really holds back the LR3's offroad potential--if I could get some decent tires for this thing it would better my '03 offroad, which is plenty good for me.
Anyway, some random thoughts. HTH