Morten,
I didn't change anything about the image format at all. I just created the Mosaic Dataset, added a raster to it (ECW file), then published it as an Image Service. I did 12 ECW files exactly the same way and only one of them is showing this black background.
I just added this code and I stll get the black background ...
mosaicLayer.Url = Url;
mosaicLayer.ImageFormat = ArcGISImageServiceLayer.ImageServiceImageFormat.PNG8;
Nullable<double> myNoData = 255;
mosaicLayer.NoData = myNoData;