I grow potatoes a variety of ways.....in garden beds, in containers, and in pallet grow boxes. They produce well for me regardless of which method I use. With containers, just make sure there is drainage because taters don't like to sit in mud. I find that loose soil that is well mulched produces the best potatoes. This is certainly not a no-till crop, not unless you already have light fluffy soil, something only a mindful long term gardener may have created.
I've only had a few problems....
...mice. Initially I left the crop too long in the ground, thinking that I had to wait for the plant to die back. The field mice feasted on the mature spuds. Thankfully a barn owl moved onto the farm a couple of years ago and most of my garden rodent problem has been solved for me. Natural, non-toxic control....isn't that neat!
...flea beetles. I've occasionally had flea beetle problems, but it's not a constant problem. They come, they go. My best solution to date is crop rotation. I move the next crop of potatoes to an area at least 20 feet away from the flea beetle population. Trying to control the beetles in place has proven to be time consuming and overall ineffective in preventing crop loss. Keep in mind that I try not using toxic chemicals on my food crops, not even organically approved ones. Toxic is still toxic whether they're from an organic source or not.
...scab. By improving my soil and being mindful of the nitrogen levels and pH, I have gotten this under control.
I mentioned that I had left the crop too long in the ground, thus the mice found them. Here in Hawaii there is no need to wait until the plants die back. When I lived in New Jersey, that's what was done. But here, no. When the plants are around 3 months old, give or take depending upon the variety, they will lose their luster and looked "tired". This signals that it's time to harvest. Rather than dig the entire harvest immediately, I'll often snuffle around the soil with my fingers, harvesting the easy to find surface tubers. After the next two weeks or until I don't find any more easy ones, I'll then dig the soil looking for the deeper tubers. I find that the potatoes stay in better condition this way as opposed to harvesting them immediately then trying to store them.