I don't know that it will be a huge problem. You're mostly dealing with shear forces; the fact that mdf doesn't hold screws as well as solid wood shouldn't be a major issue unless you plan to slam the door regularly. You could choose longer and/or larger diameter screws than are typically used, to improve their holding strength.

Depends on the weight of the mirror and how much the door will be used. It also makes a difference if the door is a hollow core or solid MDF door. I doubt if any full length morror could be successfully mounted on a hollow core MDF door due to the light construction of those doors.

If the mirror is framed, that adds weigh and difficulty of mounting. If you could just glue the mirror to the door, that might be ok.

The problem is twofold---the screws, if any, holding a framed mirror to the MDF will have a lot of stress. Two screws will almost certainly fail quickly. Four screws would last longer. Ten screws spaced out around the frame would be better.

Gluing the glass to the door and supporting it with mirror brackets---as if in a wall---would be the best and longest lasting method. It would be permanent, however, as removing the mirror will damage the door.

The other problem is the hinge screws. If the wood strip in the door is thin, using larger screws will do little good. Using longer screws is not much good either, as the longer screws would simply extend into the MDF core---or into the hollow space---if the door is a hollow core MDF skin model.

Oh, I wasn't thinking about the hollow core/MDF skin possibility. That would make it a challenge. As to larger/longer screws, I meant those for whatever fastening system was used to hold the mirror to the door, to get a better bite into the mdf -- not for the hinges.

Along the lines of the glue suggestion, I could see some cushioned, 2-sided tape being useful here, in addition to typical brackets.

The advice about the hinges is still germane---as the added weight of the mirror will also cause additional stress on the hinge screws.

If it's hollow core, just use moly bolts. The collapsible heads will distribute the force and you won't have to worry about any threads in the MDF loosening up over time as might happen if you just used a regular screw.

Also check the screw lengths on the jamb side of the hinges. If it were mine I'd make sure there is a 2 1/2" screw in each of the hinges going into the jamb.

regrads, rredogg

A plate glass (1/4 inch thick morror is heavy, bu the typical single strength mirror is not that bad at all.
The same hinges and screws can support a solid door as a hollow core, so forget about the weight.
For a solid MDF door coarser threads are better, and for a hollw door just use molly anchors. You will have better luck with a setting tool than relying on the anchors to bite in and allow the correct upset.