I have seen the white dots referenced in this thread. Here's my experience with them.
The first image is a series of images stacked using one of the composite options so the shutter speed reads 15s however it was probably 10-20 exposures of 15s combined in camera.
This is the original unworked DNG exported as jpeg for this thread
The next two images are crops of the above image after post processing. You'll notice the underexposure on the land sections in the main image so in post I pushed a bit harder to get the detail. The following image is a crop of the bottom left section to show the dots and hot pixels at their worst. This was the first time I'd seen the dots.
This crop is from a second copy where I did not push so hard on the details and the dots/hot pixels are still present but less obtrusive. The land sections of the image were unfortunately a bit soft to deal with the dots so the image is for the interwebs only.
The white dots are very hard to see when the image is viewed on a white background, but they are most certainly present. When I discovered these I thought wow, I've got a lot of stuck/hot pixels so I used the pixel mapping function and got on with it. However I haven't been doing a lot of long exposures of late and hadn't given it another thought until I saw the white dot comments aired again. It got me wondering so I went to some long exposure images and went looking.
I think the pixel mapping did help a bit but not completely. The dots are still present, most obviousl in the darker sections of the image but present in the lighter sections too.
To ensure you could see the white dots I went to two different long exposure images, made heavy crops and cranked up the brightness, contrast and clarity sliders in LR6.
This is an astro tracer image and shows the white dots on the ground (blurred from the sensor motion). The crop is from the bottom right corner of the frame.
The second is of the top left corner of the frame showing the night sky and trailing stars. This image is a straight bulb exposure.
My K-1 needs to be checked for the mirror issue so I will ask about the dots when it goes in.