Yin and yang...

Its not unusual to get only a few spuds per plant. For the space they demand, their relative yield is poor. With time and working the soil, your yields will improve (just remember to rotate or you'll have problems). Wherever you plant them, they need the heavy application of old manure or they just won't perform. People with poor soil can benefit from growing a green manure on the previous year's spot as well (winter rye, etc) to loosen and enrich the soil. As for the rotting, could be too much rain, which means you'll need to watch next year's crop and soon as they've flowered and begin to die back, you'll need to get them up as there'll be no more growth underground.

Same with garlic.
The bulbs you want to plant for next year do need a short rest before planting, which could be late September or early October. As for bulb size to plant, we've all had varying success with both small and large cloves so mark out areas where you'll plant smaller and larger cloves and next year note what sort of yield you get from each.

Other then the size I would have said that 5-6 per plant was fair. Others may get more but I suspect just as many will get fewer. 
Planted some last year and I doubt I managed 2 decent ones per plant. 

I have reverted to planting in large pots/tubs as I do not need a lot and find I get better overall results.