Excellent, Inexpensive Water Purification!

Use Katyden Filter on Rain Water and Water Collected in Humidifier...

and catching the steam?

You would need to run it through a good filter like a berkey. The only benefits you would get from this are that you wouldn't need the extra fluoride filter and you could get water if the water supply shuts off. The thing is that if the water supply shuts off, power is probably off too. You also need to replace the dehumidifier bucket with one which is rated for potable water.

Your best bet is to get a top notch filter like a berkey (or a katayan pocket filter if you want it portable) and then deal with getting the water on your own.

If you want the ultimate cheap water solution, put a potable water barrel under a downspout, screen the water coming in to remove leaves and drop a silver dollar in there. This isn't the best method but it does work, set up is less than a good filter and operating expenses are minimal (replace coin every few years).
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Besides the possible contaminants, the water is distilled. This isn't the best drinking water in the long run unless nutrients are added to it. For those pursuing a cheap filtration method try looking into solar stills.

all research i have done on this points to a high level of heavy metal contamination as well as massive amounts of bacteria. it is difficult to filter out all of the contaminants. this water is referred to as grey water and is suitable for other purposes, but not drinking.

http://en.wikipedia.org/wiki/Dehumidifier
Potability

General dehumidifier water is considered a rather clean kind of greywater: not suitable for drinking, but acceptable for watering plants, though not garden vegetables.[2][4] The concerns are:[4]

* the water may contain trace metal from the solder, most significantly lead (which is quite damaging), but also copper, aluminium, and zinc;
* various pathogens accumulate in the water, particularly due to its stagnancy, including fungal spores; unlike in distilled water, 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.

The trace metal poses a danger if used on edible plants, as they can accumulate; however, the water is otherwise usable for irrigation.

One can make food-grade dehumidifiers (avoiding toxic metal and keeping the collection tank clean), which are called atmospheric water generators.

is a great idea. Thanks