Thanks for sticking with me! I contacted Leviton yesterday afternoon, and explained the problem I was having. The tech support rep told me that if I have checked my connections, and they look fine, then the flickering is not a cause for alarm. He tried to explain that the switch has a small capsule "sort of like a neon tube" built into it that illuminates the switch. He said that like many neon signs you see, some flicker, most don't. He stated that evry once in a while, you will come across a switch that flickers -nothing really wrong with it, excpet that the 'capsule' has some inconsistency associated with it.
Well, after all of that, I will probably replace it anyway!