Phone connected to charger full time - never sleepmode - any danger?
Depending on the phone, my biggest worry would be screen burn. I have a Samsung Galaxy S Vibrant and I have screen burn at the top of my screen from the time and the notification bar.  A screen like a Super AMOLED is actually a lot easier to get screen burn then I thought it would be. It is actually pretty annoying now, I have to limit the background images I use, otherwise the burn is really noticeable.