As a complete smartphone virgin, my first bugbear is an ergonomic one. It's with the Menu and Back touch-"buttons" to the left and right of the Physical Home button at the bottom below the screen proper. You have no idea they are there and they only light *after* you have hit them. So completely camouflaged. I know I will get used to "knowing" where they are but it's poor design and irritating.
I also don't like that I can't mount the SD card or the phone onto a Mac desktop as I could with my last feature phone. The workaround is with Android File Transfer but it's clunky. You certainly can't do things like renaming files on the phone or do much housekeeping - from the computer. I rather suspect this is all Apple's fault and not Samsung's.
I've found the software occasionally buggy and it has given me problems and necessitating force shutting down of some programs from time to time but so far everything has been soluble.
The OS is still a steep learning curve. I am still finding it difficult editing the main screens and app screens to get them as I want and that Multi Window panel, I am so far unable to add things I want to.
My buying decision was made when I saw the Note 2 about four months ago (at Samsung, London) and I anticipated the Note 3 and waited. The choice was made almost - but not entirely - on the existence of the S-pen. and the screen quality and acreage. I haven't been wrong about either. No buyers' remorse.
Plus of course iPhones have superseded the position occupied by DOS IBM PCs once. Safe and very boring because "Nobody ever got fired for buying IBM". For this and many other reasons, I wasn't going to get an iPhone.
I've been using my Note 3 since September 24. It's fun. I have yet to get into one of its primary functions for me which is controlling cameras. But for a whole lot of other stuff - I already have no idea how I did without it.