A work colleague asked me why her potatoes were hollow in the middle with a dry black soot inside. I suggested it might be a nutrient deficiency. It prompted me to look up potato problems and this is what I found.
Hollow heart occurs when potatoes grow too fast because as a result of too much water or too much fertilizer. Cavity can be discolored and lined with powdery decay, verticillium fungus. Cut away the brown areas before using. Fertilize plants early when tubers are about to form. Avoid planting varieties that develop hollow heart: Chippewa, Katahdin, Mohawk, Irish Cobbler, Sequoia, Russet, White Rose.This webpage also covers a range of other problems, although not in great depth.
As always I checked the Gardening Australia website, but alas nothing specific about potato problems. Then I found this PDF (American), which again is somewhat general, but gets you on the right track to ask your local nursery about some solutions, depending on your problem.
Our potatoes in tubs have popped up nicely and look healthy and green. I just hope hollow heart won't be a factor, as the tubs contain a good deal of compost. I guess we'll just have to see.
By the way, if you're looking for a way to grow potatoes in a small space, you might like to see what Josh Byrne set up; it's a potato cage!