Though tautech basically said it, the answer is no. Modern TFT LCDs don't suffer from the same kind of burn in that plasma screens or OLED screens, so the only issue with leaving it on long term is the normal concerns with powered up electronics (so very little) and then maybe backlight aging? If it's a CCFL maybe that's something, but if it's LED backlit, then you're going to be looking at electrolytic caps drying out as being probably more of a concern than anything screen related in terms of high-uptime longevity.