Below are shots taken with the Tamron 18-250mm F/3.5-6.3 at the 135mm setting using an EOS 20D. The images are unedited 100% crops from the original images taken from 3 places in the frame. The first crop is with the target in the center of the frame. The second crop is with the target about 50% of the distance to the edge of the frame and the third shot is with the target in the top left corner of the frame.
As you can see, center sharpness is pretty good at both f5.6 and f8. There is a drop off in image quality as you move towards the edge of the frame and there is a significant sharpness loss in the corner. Stopping down to f8 definitely improves image quality both at 50% of the distance to the edge and especially in the corner. Slight evidence of chromatic aberration can be seen in the corner shots. To give you a standard of comparison, the crops below were taken from images shot with the Canon EF 70-300/4-5.6 IS USM.
The image on the left is from the center of the frame at f5.6, the image in the middle is from the corner at f5.6 and the image on the right is from the corner at f8. There really isn't a great deal of difference between the center of the images shot with the two lenses, but I think it's clear that the Canon image quality is higher in the corners of the frame. Of course the Canon lens has a much shorter zoom range and is slightly more expensive.
[Note these images were taken under different lighting conditions from the above shots at 135mm, and the color balance has changed a bit]
At 250mm the story is much the same as at 135mm, with good center sharpness, even wide open, but with diminishing image quality toward the edges and corners.
As you can see, sharpness decreases away from the image center and some chromatic aberration is visible. Again shots from the Canon 70-300 are shown below"
Again it's clear that the Canon 70-300 is better in the corners, though center sharpness is pretty similar.