How to identify damage on my dslr mirror?

I'm being paranoid here. I read about cameras having coating on their mirrors and that touching the mirror would cause permanent damage. So how do I go about identifying any damage to my mirror. Wheb I look through the viewfinder, it's clear and there's no smudge or scratches. But how can I identify hidden damages? Btw, i'm using nikon d5200

You don't really need to worry about damage to your mirror, even if it does get damaged (which it hasn't if you're looking through the viewfinder and seeing nothing out of place) then it still won't effect the final image.
However you do need to be careful not to damage the image sensor, which is positioned behind the image. All that the mirror does it re-directs the light coming through the lens into the viewfinder instead of onto the sensor. When you take a shot, the mirror gets out of the way (the click noise you here) and then the light can go to the sensor.
The way you check if the sensor is damaged is so do a longer exposure (say 2 seconds) and move the camera around. If you see anything that looks like it isn't motion blurred then it could be one of two things.
1) It could be dust on your sensor. DO NOT remove it yourself, go and get it professionally cleaned as if you damage your sensor (i've seen it happen with the tinniest of things) then its an expensive fix).
2) It could be damage to your sensor, if you get it cleaned and it comes back with stuff still on it then its damage and you need to replace the sensor.

The mirror is a very lightly and thinly coated front side mirror. You can scratch it easily. If you get your finger print on it, it can corrode.

Take your lens off and look at it closely. Do you see any damage? If not, you are fine.

There's no such thing as "hidden" damage. It's a front-side mirror. The important part of the mirror is facing you.

About the only way the mirror can be damaged is by you sticking your finger or some other object inside the mirror box when the lens is off. Otherwise, during normal use its all but impossible to damage the mirror. So stop worrying about a problem that doesn't exist.