I have the K-01 and have used it for video (both manual and auto).
I believe none of the pentax APS-C current cameras have continuous autofocus while shooting. However, at least with the K-01 and newer models you can autofocus by pressing a button while filming and the camera will adjust the focus accordingly as long as you're using an AF lens.
I have preferred overall though to use an old pentax manual lens for video.... it's quieter, less hunting so smoother transitions, but you would have to rely solely on focus peaking via the lcd screen with the K-01, which in bright sunlight can pose problems sometimes. Obviously you could instead pick a pentax model with optical viewfinder to make manual focusing in bright sunlight easier. Alternatively this is a hack some have tried:
The overall image/video quality of the K-01 is suberb and it is such a fun quirky camera to use, small albeit with a solid feature set ie. external audio jack, hdmi out, focus peaking to name a few.
I do however wish Pentax would bring the K-01 into 2015 by adding the following features for a successor:
Wifi connectivity
Video continuous autofocus
Viewfinder (or at least a hot shoe add-on)
Flip screen (being greedy!)
Weather sealing would be great but with these last 2 I'm just being greedy!
This in my mind would represent my perfect camera in 2015: relatively small without compromising image quality, robust, access to all legacy lenses, with current feature set to blow the competition out of the water.
PS. The new K-S2 might be worth a look-in for you has all my "extra features" apart from continuous autofocus, you get a lot of bang for buck - I'm seriously tempted by this beauty!