I'd agree with DA01 here. It's far more likely that your wall isn't perfectly flat rather than the mirror being distorted.
The simple way to test this is to get a spirit level - or anything with an edge you know is true - and lay it across the mirror. If it doesn't lie flush then the mirror is warped. You can do the same with the wall.
You'll probably have an easier time using a picture hanger than a screw, and it will leave your wall in better shape when you remove it. Picture hangers transfer the downward force into pressure into the wall because the nail is mounted at an angle. The screw, on the other hand, is being bent because you're acting as a lever, where the stud is the fulcrum, the drywall is just empty space, and the wire is the force applied at the end. Even if you get a stronger screw, you're still placing a significant twisting force into the stud.
You can't use your typical picture hanger for a task like this. The small hangers that come in most kits are rated to only 20-30 lbs. However, you can find hangers like this one that is rated to 100 lbs (and I'd still use two of them, since it will make adjusting for level much easier and reduce the risk of failure).
The other option is called a french cleat which are two interlocking rails, one that attaches to the wall, and the other to what you're hanging. As long as you install them both straight and level, you don't need to adjust the mirror for level, and it distributes the weight across a larger area, reducing the risk of a failure.
Best Answer
If it's very long, I'd suspect that it's being physically distorted during the installation process since the glass itself is flexible enough to distort the image without breaking first. To correct it, you need to make sure that the mirror is as straight as possible - use shims.
If it's along a wall, the mirror may be following the contours of a slightly uneven wall. You can shim the back of the mirror in the hollow spots to correct this. Masking tape (ideally the blue kind to protect the mirror) can be used in the low spots to build up sufficient support for the glass. Thicker shims can be used if you find the hollow spots to be very thick.
It's it's in a frame of some sort, either the frame is not straight, or it is sagging/distorting too, or (if the glass is sufficiently loose int he frame) the mirror itself is just distorting as above. The approach is basically the same - shim the spots that you need to push forward.