I've noticed the Note 3 won't focus quite as close as the Note 2 did but it might be off by just a few cm. I took this shot yesterday:
. | Flickr - Photo Sharing!
As for HDR, the camera software built in does a far better job of rendering than the trickery recently introduced by in Snapseed. The Snapseed HDR is great if you're into the really tacky HDR stuff but the Samsung camera HDR came out looking much more natural:
Random chair shot | Flickr - Photo Sharing!
Overall, I have to say I'm very impressed with the camera on the Note 3 after using it for a while. The only thing I'd like added is manual focus control like they have on the G2. The manual controls on the G2 almost had me swayed.