I have used the Tokina 12-24/4 with my D200 for many years. It is an excellent lens, and I never had a problem with it. I don't think that a UV filter serves any useful purpose. In fact, some of the "vignetting" in #1 is apparently caused by the filter. Regarding the over exposure in #2, I have no explanation. Perhaps the exposure compensation was set incorrectly, or the picture was part of a bracketing sequence.
The vignetting in the first image looks like the lens hood is not fitted correctly. I sometimes get the same thing when I fit it in a hurry. Make sure the dot labelled IN on the hood is aligned with the dot closest to the front of the lens when attaching the hood, then make sure it is fully clicked into place.
If you look at the vignetting in the first image, it is predominately on one side of each corner - not balanced. As stated by Steve, this is the classic appearance of a petal-shaped lens hood that is not correctly fitted to the lens - likely not fully "clicked" into place.
Unfortunately, I have nothing to offer on the apparent overexposure in the second image.
That's a pretty bright scene. The EXIF data shows the photo was shot at f8, 1/250, Pattern metering and 0 exposure bias. It looks like about 1 stop over exposed. Have you tried another lens on the same scene? Your first photo was taken at f9 and 1/320 sec.
As to your vignetting, I think the Tiffen filters are pretty thick. While I think this particular scene can benefit from a UV filter you should get a thinner filter designed for wide angle lenses. That should help. I would probably advise against using any filter with this lens.