Is there a smoker in the house?

Looks like there is residue left on the door and kitchen grease or smoke is condensing onto it.

Try cleaning it with isopropyl alcohol.
If that does nothing, then I would try varsol.
Try it in an inconspicuous place first just to be sure it will not damage the finish. Also do not use it on plastic/rubber.

Once good and clean give it a coat or two of car wax.

I would check to see if the door face is cold.
Could be the insulation has gotten wet over the years and is not doing a very good job anymore and that is causing excessive condensation.