That's a real nice setting that you have there. The house looks amazing and the pond will only make it look that much nicer!!!!
I wouldn't worry about those stumps too much if they are going to be in the water and not part of the dam. You want to dame to be as free from anything organic as possible. No top soil in it and no roots or branches that will decay over time. From the picture, it looks like you are on the side of a hill and the water will be coming down the hill to fill the pond. How much hill is above the pond and is there any concern of too much water coming down and overwhelming your spillway?
The number one reason a dam fails is water running over it. The water erodes the dirt and it just keeps working it's way down until all the water is gone and you have a big gap in your dam. I've seen it happen about a dozen times around here and I'm sure I'll see it again. A big rain will put a lot of water in there quickly, you need to be able to get it out of there just as quickly once full.
Another concern is how tall will it be and how steep will the dirt be on the dam? You never want trees growing on your dam because their roots will tunnel through the dam and over time create a path for water to travel through the dirt in your dam. Grass that is maintained and mowed a couple times a year is a great way to protect your dam from erosion, which means it has to have a slope that you can mow. Rock, riprap and gravel are even better, but very expensive since it has to cover a lot of area and be thick enough to protect the dirt below it from erosion.
Eddie