Water quality
Things to consider include water parameters, ph, nitrites, and nitrates (least harmful). Obtaining the right water parameters means healthy koi. Invest in a good-quality water test kit. Major fish health concerns are avoided if the water is good.
Based on experience, most hobbyists are concerned about ammonia and nitrites, and for koi, the major drop in ph is one principal cause of fatality. Even with the right feeding and filtration, I would always recommend a constant partial water change at least once a week -- the more frequent, the better.