OK here is an example, this is a still clip taken from a video. The camera had been shooting outside for about 8 minutes on a Texas afternoon:
http://i73.photobucket.com/albums/i202/richtrav/videobanding.jpg
To be fair that is about as bad as it gets, but it looks worse in motion than on a still.
Here is another, less egregious example from a timelapse taken at night, where there is a distinct band down the middle (this was taken at 5500' elevation in Mexico, so our nice toasty Texas sun was not the culprit)
http://i73.photobucket.com/albums/i202/richtrav/IMGP2053.jpg
Really if these occurred after long sessions of shooting video I wouldn't complain, but it crops up pretty quickly in the Texas heat (did the same in Manzanillo last week too). Aside from this issue I love the camera and its pictures and videos. I know some have blasted the 1536 mode but I love the flexibility it offers (being able to crop the top and bottom wherever you want, pillarboxing it for a 1080p screen or boxing/downsampling for a supersharp 1080 x 720 video or somewhere in between, the ability to control the sharpening when it gets downsized to 1280, etc etc). That is of course if you don't mind post-processing; if you want easy good looking video straight out of the camera set it to 1280 with no adjusting to the presets and let 'er rip. They're noticeably better looking than the default videos from Canon's T1i or Nikon's d5000/90
Sure I wish it produced the quality of a 2mp downsized still (who doesn't?) but no camera in 2009 that costs less than 5 digits can, including the 5D or GH1. I poured over many sample videos from all those cameras and to my eyes the K-7 can keep up with either of them in decent light. The stills extracted from the 1280 mode are usually good enough to be used straight out of the camera, and 1536 stills are even better if downsampled to about 1200 x 800.
The explanation falconeye gave for the video implementation makes perfect sense - I used to have an old Kodak DSLR with no AA filter and it produced similar images: sharp but with some moire patterns present. By sampling every 3rd or 6th pixel the K-7's AA filter would not be able to do its job of reducing moire. The "Christmas light" speckles are easy to deal with and I think I remember even seeing a program that can deal with it automatically; on the other hand, the wavy luminance moire that you rarely see in windows or on clothing is very hard to treat (though to be fair I've seen moire on other video cameras too, it even crops up on TV). I'm still tinkering with the settings for video: what looks good on a computer screen and what looks good on a typically preset HDTV are often pretty different. Turning the sharpening down helps the artifacts in 1536 mode, and making use of the easy to access contrast and hi-low key buttons can really squeeze more dynamic range out of a scene (or conversely be used to "crush" the darker regions to get less grainy looking videos indoors).
Speaking of all this, does anyone know how the K-7 is outputting videos from the HDMI port in 1080i mode? Before the video starts it appears just like it were in 720p mode but once it starts playing the image contracts slightly and looks a bit crisper. Is the K-7 keeping the width at 1536 pixels and stretching the height slightly to a full 1080 pixels? Whatever it is doing looks good, though panning does cause some stuttering. I'm guessing the stuttering is a limitation of the K-7's playback circuitry: it's not in the actual recorded video, nor present when being played straight off an SD card onto a computer screen.
Bottom line, yeah I think I'll give another K-7 a try to see if it performs better. I don't have to have perfection, just something I can use for more than a few minutes outside in summer