I am going to comment on the first image and crop. I am going to estimate that the fence posts are about 10' apart, so the distance to the woman sitting on the bench is about 40 feet? At 8mm, with a target range of 40', the field of view is 120' x 80' (see the dimensional calculator at
http://www.tawbaware.com/maxlyons/calc.htm). The K5 sensor size is 4928 x 3264, or at that range each pixel is 0.024 feet or about .3 inch. If an average face is (I don't know) 8 inches wide, so that would be 24 pixels. How much facial definition can you get in 24 pixels of width? Not a whole lot of resolution there. Actually in the cropped image you can tell that she is Asian, looks somewhat tired - pretty good resolution for that. Take a look at the gentleman holding the child, and the child's face and hair style. At this distance for a Ultra Wide lens (in a cropped shot) - this is not bad at all in my opinion.
Where I am going here, is that with ultra wide angle lenses, you are pulling in a tremendous amount of additional scenery around the edges and pushing the center back away into the background to accommodate this additional area. So you have a lot more scene, its wide - however you have the same amount of pixels with which to record the scene. Therefore, each pixel will be recording a lot more information than say it would be with using a 30mm lens (normal for a cropped camera).
For the sake of argument, lets use the same scene with a 30mm lens. FoV would be 30' x 21' and each pixel would be ,07 inch, or for an 8 inch face 114 pixels across. This is nearly 5x more definition in just the horizontal axis, or 25 times more resolution in area.
The moral of this is, you are not going to get the resolution you are use to when you have an ultra wide lens mounted. There is that word again - ultra. The resolution and definition are being traded for a tremendous larger scene width and height - scene area. It has to go some where - and where it ends up is in the pixels. It does not mean that the lens is not sharp. You are just using the wrong standard of comparison.
As others have said, where are you focused and what is the aperture, thus your hyperfocal depth of field. I am thinking that the monkey bars might be a tad sharper, but then again it all depends on what you and the camera were focused on.
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The last set of images. Lets assume that the sidewalk is creased at 10 foot intervals, so you are about 70 feet from the street sign. In the crop image, you can read the street sign 28 th Ave, also almost able to read the walk/don't walk instructions on the push button and nearly able to see the license plate on the car. [If this was a TV show, I could zoom in again, sharpen, apply a (brand new from the MIT lab, beta version that i just received this morning from my friend) pseudohyperspectral sharpening mask, zoom again and then clearly see the license plate and that the owner is behind in his new registration tags, and parks at the beach since it has seagull poop on it. But this is just a mere plain Jane pedestrian Pentax camera, not an ultra professional Nikon or Canon. (just kidding).] If the focus was anywhere near that plane of focus, you are doing pretty well. How high is the lettering on the street sign? I am going to say what - 4 inches tall? You can almost make out the green sign across the street above the parked car with the license plates.
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Now if you are going to really make a comparison, then use the 8-16 at 16mm compared to your 16-50 lens at 16mm. Apples to apples. Then you are going to have to make a slight adjustment since the 8-16 is at the top end of its range, while the 16-50 is at the bottom end of its range. What you don't know is how each lens is optimized within its respective range of focal lengths. Take 2 images, focused on exactly the same point, using the same aperture (f8 should be a good sweet spot for each lens) so that you will have the same depth of field, at the same focus - infinity would probably be best. That, I think will be the best test - with a relative known "good" standard as a benchmark. My guess is, that they are going to be pretty equivalent. Any slight difference could easily be attributed to how each lens was optimized.
Bottom line - I think that the camera lens combination is pretty damm good!!!! (if this is a bad copy, I would like to see what a good copy could do?)