The touch screen on my Lumia 520 (with Windows Phone 8.0) recognises touch gestures even before I'm actually touching the screen.
How do I disable this? It might be a stunning feature for some of you but I am not used to it.
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Sounds like you may have Super sensitive touch enabled. This lets you use your phone with gloves, but can be annoyingly sensitive if just using your bare hands.
To disable this, go to Settings → touch, and set "Touch sensitivity" to normal.