What problems can I have if I try to dry up the parging of a wet wall using a plumber's torch?
You mean other than burning your house down? Yes, rocks that have water in them like to explode sometimes when you heat them. Use a fan and come back next week (seriously, if the wall is saturated it could take months to dry out).

Also, it's going to leave scorch marks, which will be less than helpful.

More also's: one of the by-products of combustion is H2O.