I'm currently doing the same method only with potato bags (heavy tarp plastic bags with an old fashioned pajama butt flap at the bottom for easy harvesting of the potatoes). Plants seem to be perfectly happy in them, although they take a lot of water due to the entire soil column basically getting full sun and warming up.

I tried the trash can this year. They are doing great, have grown out over the top. I don't know what to do now, just wait I guess.

Well, I get volunteers each year, but I pulled those up this year and have mine in big tubs from Biglots.
I started mine with about 1/3 of the tub filled with soil, then top with homemade compost from time to time.
Bottom of a drained barrel? They do need some soil to grow in! Nancy

If you are asking about potato towers where you plant in a deep container and slowly fill it to the top hoping to get potatoes from bottom to top, many have tried it and few have succeeded. Search potato tower or potato bin on Gardenweb and you'll get a lot of stories. I started a thread last summer about my experience, and one of those who responded got a nice yield from russet potatoes he grew for about five months. The thread includes lots of photos and stories. Follow the link below if you're interested.

Here is a link that might be useful: Tale of two potato bins

Last year I made rounds of chicken wire, about 3' wide by 3' tall, lined sides with straw, put soil on the bottom, planted taters, mulched with soil or straw as they grew. They looked healthy for a long time, but then kind of slacked off.... yield: nothing! I've grown potatoes in the ground successfully for 15 years. Granted last year was bad for those too. It was disappointing b/c articles about this method are so enthusiastic.

That was almost exactly what happened to my rose Finn fingerlings except that my tower was 3.5 feet wide and 3 feet high and I got 6 marble size spuds. Could some creature have come from underground and eaten them before they could grow? The tops grew four feet tall and I have a couple of great mousers. I did at least get a crop with other varieties in plastic tubs with bottoms. I wish someone could explain what happened.

We tried the straw method in a box and didn't get any potatoes last year. My guess is that straw doesn't dry out like dirt and though we got 3-4" tall stalks, when I peaked in, the center was wet, stalk slimy and thin. I was told you're supposed to water from the bottom if you use straw but you can't help it if it rains.

We will try dirt this year. Disclaimer- last year was our first potato attempt so we really don't have a comparison.

I'm doing something similar this year, after swearing I'd never plant potatoes again.

This year, I'm using "better" growing medium (peat moss, vermiculite, perlite & compost). In years past I simply used topsoil and never had any luck.

For my container, I'm using an old metal, Brinkman BBQ bullet smoker. So far, so good.

Lesuko - that's supposed to be the advantage of straw, that it holds in the moisture, which potatoes like. Of course, with too much moisture, they rot, but that seems to be more of a drainage problem than a mulch one.