I recently got an S4 Mini and my only problem with the device is what happens when I plug in a set of headphones/earphones.
Plugging in earphones will often open up S Voice at random intervals. This happens when I use the standard white earphones and when I have S Voice disabled. This happens with the earphones that came bundled with the device and also with several different after market alternatives, one of which resets my phone the instant I plug them in.
Other issues include my screen randomly scrolling, music starting and stopping of its own free will, and often fluctuations in volume, all of which only happen when earphones are connected.
I realise there are issues with earphones of a certain ohms count, but like I said, this also happens with the pair that came bundled with the device.
I have the most up to date version of Android that the device allows and I have no third party apps installed that could cause the problem.