Although I didn't purchase this armband from here I thought I would post my review on it.
I use it in the gym when I am on the cross trainer, bike, treadmill. I can confirm that this armband does not move at all once it has been tightened up.
I sweat a lot in the gym and this armband never lets the sweat through on to my iPhone, instead it stops on the back of the armband that is in contact with my arm. If it does get sweaty, it is just a simple matter of washing it in warm (but not hot) plain water and no soap. I emailed the manufacturer and they told me this.
The front of the armband does not have a plastic cover over the area of where the iPhone screen is, and as such the touchscreen operation of the iPhone is not impeded.
If you are a sporty person who wants to wear their iPhone on their arm when exercising/working out, then this armband should be at the top of your list, it is well worth every penny, superb product!