I have the same problem and it is about to get me as riled up as the auto correct did on my SIII. Rage. Rage incarnate. I have a "Display and Wallpaper", is that what you mean my "Display"? And I don't have a "Smart Rotation" anywhere that I can find, though I do have a "Screen Rotation", which is and has been on (green check mark) and a "Smart Stay" that keeps the screen active as long as someone is looking at it. I don't think either of those is doing anything though since I turned "Screen Rotation" off and as suspected, it stopped rotating. Back on and the screen takes about 2 very long seconds to actually turn. My SIII did it with only a slight delay, just long enough for the phone to know turning the phone in a different direction was not an accident.
Also, I did not get any real directions. Is this something new? I know I can get them online, but not having the little booklet to look stuff up in kinda irritates me too. I am guessing that they finally figured out that most people never read them and stopped printing them to save money.