Sears Ultra Free powder leaves a deposit on my washer's drum, though not as severe as what you described with Tide. An extended sanitary-temperature wash with citric acid removes it. Citric acid ought to be safe, since a package of expensive Miele descaler I bought contains just that. Since I've been using STPP (in the washes I do, not the rest of the family's), the drum is staying pretty clean.

I used my HE Top Load machine for the first time last night. I used the Gain HE powder. I didn't wipe the drum to see if it left a powder residue though. I did seem to notice a sort of brownish, very light, line about 4" from the bottom. I am not sure if that was the water level line or something else. I will wipe the drum this evening to see if the gain left a powdery residue on the drum.
I have seen quite a few very positive remarks about the Sears Ultra Powder Detergent with OxiClean for HE machines. I was thinking about trying it as my wife hates the perfume smells of the gain and tide he powders. Does it hurt the clothes to use the Ultra with OxiClean all of the time?

Residue is likely from the precipitating water softeners that may be in non-phosphate detergents nowadays. I've been using Tide HE powder and Gain HE powder for more than two years. I don't get any residue from either one ... but I also have been adding STPP for the duration.

I can only think that it is precipitated minerals from hard water. Some detergent formulations are better at sequestering the hardness in solution than others. Water chemistry must also have a lot to do with it. Someone elsewhere posted that Charlie's Soap did not leave a residue, even though it's mostly sodium carbonate (precipitating softener), while other more mainstream detergents did leave a powdery film.

Use the product that does not do this, as it can't be good for your clothes or your machine.