Okay well. Lets look at requirements for both species:
Turtles: At LEAST 10 gallons per inch of shell, otherwise you are in for HEAVY maintenance. I have kept turtles since I was 5 years old (yes, kept them, not just found them and put them in a box) and they are real poop machines. Not only do they poop a ton, but they will eat a ton. You need to get them a good stick/pellet and fresh foods such as shrimp, tilapia, watermelon [a good, sparsely given, treat], other fish and seafoods, no mammalian proteins. A good vitamin on their food once a week will help with shell development and overall health. NEVER give feeder fish because, not only do they bring disease, but they make a GIANT mess of scales ALL OVER the pond when they are eaten. Plus, my turtles don't like the heads so those make a big mess and rot if you don't get them out right away. Water needs to be 72-75*F. Too cool and they have major metabolism problems, too warm and they will never bask (which is a BAD thing). They MUST [repeat MUST] have an area where they can easily get out of the water [easily!] and bask under a heat light. The basking site should be around 95*F. Also, they must have a UV light or they will DIE. Tube UV is okay but is ugly and very uneffective, also it must be within 12 inches of the shell to work. I would suggest combining UV and heat with a Self Ballasted (externally ballasted ones do not get hot) Mega-Ray bulb.
http://www.reptileuv.com/
Koi: These fish have nearly no defense against predators... At all. These fish are big poopers and require a ton of space (I think I heard 400g each somewhere) to keep waste at easily manageable levels. They are voracious eaters (which could be a problem to the more shyly eating turtles) and can be overfed (which is a problem seeing that they will probably never let the turtles eat).
I think that you are asking for problems combining the 2 but, as long as the turtle's requirements are met (honestly, I am not much of a koi person) then I would be fine with it.
The main issues I predict will be turtles tearing up the koi (they might not be able to eat them, but they can chew the sh** out of them), the turtles never getting to eat because the koi will eat their food before they can, etc.