I'm assuming that it's jailbroken since it's in this forum? If so then just remove each tweak one by one, testing to see if the screenshots keep happening each time you remove one, until you find the tweak that's causing it. Or you could restore and see if it's the phone and not the jailbreak/tweaks.
I thought it might have been activator at first too but he said he tried ilexrat and the problem renamed so I ruled that outMess around with activator. Somehow the screenshot action may have gotten switched to something such as a home button click, or certain place on the screen touched.