2014 5k image persistance

This is my first iMac and it has had persistant problems since I have got it. I have been told by Apple that everything is software related so I just have to live with the issues, even though what is going wrong doesn't seem to effect many or any one else.

So last night I decided to watch some TV shows that I have recorded off HDTV on my iMac. So I put on my headphones and went full screen and along the right side of the screen where many icons have been parked, I you could see the ghost of them on the screen. Things that were white glowed on the screen as if you were seeing through the video. Sadly that includes my network drives and the text titles for each of them.

I have read this is image persistance. I have AppleCare so is it worth driving over to the Apple Store to get it fixed. How long does it take for a screen to be replaced by Apple? Am I going to introduce new problems if I get this done?

I have read posts here that the screen issues are known to Apple and its not a matter of if but when the screen will go wrong. Should I just be trying to minimize anything white on my screen that is stationary? is it something that I am doing wrong or just the way that it is. The iMac gets used daily but I mostly try and shut off the screen when not using it. I don't turn the iMac off.

Any help of suggestions would be appreciated. It is my 'lemon' iMac telling me it needs to be replaced.