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.
So, I went with the mastic.
Bad news - between not boing thick enough, and the fact it's pressboard, I didn't feel confident using any kind of screws to hold the door. I went with a pure mastic solutions.
Good news - this in fact a door, so you can take it off. This lets you keep it horizontal, and put weight on it to help the glue hold.
So, I took the door off the hinges and laid it flat. I marked off the perimeter of where I wanted the mirror with blue tape (Blue Painters tape is one of my favorite tools). I thought the surface was a bit plasticky still, so I scuffed it up some with some sandpaper. I put the mastic on the mirror, trying to keep the inch from the edge. By the time I was done with my pattern, I was almost done with the mastic tube, so I just emptied it. I put some 2x4s and other heavy things on top to help the glue hold (another advantage of having a mirror it on a door). I let it sit for the recommended 48 hr set period and put the mirror on.
The only downside I see so far, is the weight on the door. It seems stable, but the wardrobe didn't seem 100% level. What was OK before, what closed fine before, now stays open a bit with the extra weight. My next subproject is re-leveling the wardrobe.
Best Answer
I would suggest hollow wall anchors. Four of them, two per side and six to eight inches from each end. These anchors come in different grip ranges so you have to have one that is matched for the thickness of the door panel (likely 1/8") plus the wooden frame of the mirror. They can hold a reasonably good load and they have amazing pullout when used on paneling and hollow doors.
An example of the anchors is here https://www.boltdepot.com/fastener-information/Anchoring-Products/Hollow-Wall-Anchor-Info.aspx
If you don't have enough wood frame around the mirror then you may have to use a mirror clip with the hollow wall anchors.
This suggestions though will put four holes in the door skin about a 1/4" in diameter.