1. Was that ice just holding on--barely ice at all and once the slight cooling from the mechanism stopped; instant Spring runoff? The basement is not particularly warm, you would think ice would take a while to melt.
2. In the context of other dehumidifiers and portable air conditioners that have come and gone, I have noticed that when they get old, they are more prone to ice-up. I looked up the physics of these devices and the upshot is that when the Freon (or whatever coolant is now used) gets low, it causes the coils to become too cold and so ice forms on them. On cars and on home AC units there is a port where you can add more coolant but they don't have these on the smaller units. It seems a shame that the lack of a $5 fitting prevents you from doubling the life of a $200 device by adding a couple ounces of fluorocarbons to the machine.
3. A couple of extra valves and controls will allow you to run the window AC unit in reverse (we have one like that but it was hard to find and expensive) so that it can be a heater. If they all came like this then you could use them in the Spring and Fall too. This would be good for the manufacturers because if people used the units three times as long per year, they would wear-out three times as fast and they could sell more. Also, the devices would be more useful for consumers since they can just heat the room they are using instead of firing up their furnace. Heat exchangers are more efficient than any other method when the outside temperatures are mild.
4. The ice-up on the dehumidifier made me think of a feature at Story Land. Outside of their Polar Coaster--a glacial themed roller coaster--they have a ice covered pole. Careful listening reveals that many people ask, "Where does the ice come from"? The pole just has cooling coils in it and so moisture from the air condenses and then freezes onto it.