I am a recent owner of a K-1 and find the Autofocus quite lacking. For still shots it is easy to use focus peaking in live view and get excellent results, but I found the following conditions to be too much for the K-1: dark color tones (in bright light), moving targets (with central spot auto focus in AFC).
K-1 firmware 1.41.
I use AF.C with back button focus and Central Spot and Focus Priority in the following examples (the red lines indicate the in focus plane). I placed the Central Spot on the Dog's faces (right between the eyes):
With dark color tones you just don't know what you will get. It most commonly is front focus or back focus but almost never on target.
Here is a nice high contrast subject, a white dog with a black snout running towards me. This was the only shot in focus of any of the dogs running towards me. The focus is right on target, maybe a bit front focus..
Here is a brown dog as the subject, running towards me. With the light conditions there should be enough contrast, especially with the Frisbee. But instead we get back focus. This is an example of most of the shots.
With 240 shots I got 4 in focus shots. One with a dog running towards me (the one above) and 1 of them running at 90 degrees to me. Two of the shots was with the dogs moving around each other and having high contrast between the two dogs.
With the brown dog as a moving target, here is some focus jumping sequences:
I find with the dogs, setting the spot on their heads, that I generally get back focus as they run towards me. It made me think that the auto focus is slow. The one in focus shot I got, might be a fortunate focus jump that just happens to get the right spot.
You can review some of the images yourself:
https://www.flickr.com/gp/153388317@N08/3515LG
In summation I would say there is a good likely hood of slow autofocus, or at least a significant delay between autofocus and shutter time. And I find random autofocus jumps that just don't make sense.
If anyone has any insight, I would really appreciate it!
As a landscape camera it is great! Really awesome pictures!