May seem as a trifle for someone but: have you ever noticed the bad home button response on your device running Touchwiz? I mean, when you push the button, you have to wait a years till it finally comes to the homescreen. But how to speed it up? There's a little fix for that.
This bug is generally caused by S-Voice - A voice assistant running on all newer TouchWiz ROMs. It's impossible to dispose of it, unless your phone is rooted but there's an easier way (obviously).
To be excact, when you press the home button, S-Voice is listening to the home key and literally waiting for a double-tap. As set for default, double pressing the home key automaticlly launches the S-Voice.
As you might expect now, only thing you have to do for speeding up the response, is to disable "double press Launch S-Voice function".
To do so, open the S Voice settings and simply disable this option to take the effect.