Placing the TV over the fireplace seems like a great idea. It does not obstruct, looks nice and is often the most convenient place to place in a room. However, there are serious issues that arise from this practice.
If you watch TV occasionally, then there is probably no problem. But if you watch for hours every day, make sure you know all the issues you may face.
When a TV is placed over the fireplace, it is usually located high enough, so viewers need to keep their head higher than normal.
Certainly not in all rooms. The fireplace may be low, or you may be far enough away that you do not have to lift your head too high. But if you have ever had neck problems, often from something related to it work, this aspect is something to consider as it could aggravate such an injury.
Most of us have a laid back attitude when it comes to watching TV. It is a much more natural place. Ideally you should be able to maintain a neutral / relaxed head posture to watch your TV, which will vary depending on the position of your couch / seat and so on.
The TV will be off-axis
Almost every TV on the market today is LCD. The image on most LCDs looks much worse if you do not look at it directly. Even a few inches below their center line can make the image look very different.
This is fairly easy to fix, although you will need specific equipment. Some wall mounts allow you to turn the TV down so that it is directly facing the living room.
Heat and soot damage
There is nothing worse for an electronic product than heat. Increasing the operating temperature of the TV may shorten its life.
Worse still, soot from the fire can get inside the TV, with devastating effects. The damage will be slow and over time, so the TV will probably break down sooner than it would otherwise, but beyond the warranty period. Of course this does not apply if you never use your fireplace.
Given the above, it may be time to change the position of your TV if you want to use it for many more years without any problems.