The water from a dehumidifier is really not considered distilled. It is more accurately called atmospheric water generation. The difference is distilled water is boiled which kills any pathogens.
Generally, dehumidifier water is considered a rather clean kind of greywater: not suitable for drinking, but acceptable for watering plants, though not garden vegetables.
The water may contain trace metals from solder and other metallic parts, most significantly lead (which is quite dangerous), but also copper, aluminum, and zinc. The trace metals pose a danger if used on edible plants, as they can bioaccumulate; however, the water is usable for irrigation of non-edible plants.
various pathogens, including fungal spores, may accumulate in the water particularly due to its stagnancy; unlike in distilled water production, the water is not boiled, which would kill pathogens (including bacteria); as with distilled water, minerals are largely absent, hence it is somewhat flat-tasting and therefore safe for use in batteries.