The palm may be a sago palm.  Sagos are not true palms and can produce offshoots bearing fronds from anywhere along the (living) trunk.  Sagos are quite vulnerable to a type of scale insect called cycad Aulacaspis scale.  Aulacaspis scale is white and could be what you thought was white mold spores.  Like other types of scale, Aulacaspis scale damages the plant by sucking sap.  Left uncontrolled Aulacaspis scale can kill sagos.  Repeated spray applications of a light horticultural oil will usually manage the scale adequately to save the plant, but it is important to monitor the plants and begin treating again when the scale returns.

You can see some photos of cycad Aulacaspis scale at the attached website. 
 http://www.doacs.state.fl.us/pi/enpp/ento/aulacaspis.html