I have had a lot of trouble with blurred/doubled images on my K-m and have also noticed it on my K-x.
A couple of months ago, I finally decided to send in the K-m to pentax to see if they could fix it. The double images were not the only problem with the camera, the viewfinder was also quite foggy. I got the K-m back in under a month from Pentax Canada. The doubled images are still there, but to a lesser extent. Pentax did not tell me what they did to the camera, but I do know they replaced the viewfinder, since the scratch that was on the back of the viewfinder is gone.
I bought the K-x just after sending in my K-m, hoping it would not have a problem with doubled images. I have still noticed double images at 1/60 to 1/125 of a second. I find I have much fewer double images when using the Tamron 17-50 then when using the kit lens. I think this is because to Tamron is much heavier and helps to steady the camera. I also have less double images when I remember to wait for the SR to show that its ready in the viewfinder. By using a heavier lens and waiting for SR to be ready, I have greatly reduced the pencentage of double images and no longer have to worry about my camera ruining my photographs.
I find the article on shutter induced blur on the Lumolabs site does a good job of explaining the double images that I have been experiencing.
The full explanation can be found here:
http://www.falklumo.com/lumolabs/articles/k7shutter/index.html