Not only that, but there is the environmental savings of trucking around water at 8 lbs / gallon, and of manufacturing and disposing of (or quasi-recycling -- they can't be remanufactured, like glass or aluminum) hundreds of PET bottles.

What does it take to separate the CO2 in the air from other gases? A centrifuge of some sort -- basically blowing air in a cyclone?

I wonder how difficult it would be to reduce a CO2 collection device to the size of a coffeemaker.

No it's not a centrifuge, CO2 is a product every air liquifaction plant. Air Liquifaction plants mostly produce oxygen and nitrogen by compressing air, cooling it, letting it expand, compressing it... CO2 liquifies at a higher tempature than oxygen and nitrogen so CO2 is a product of all plants and it is very cheap due to a lot of supply. Price is under $1 a pound $0.30 if you're buying railcars.