photozone.de review of Tokina 12-24 DX
At 12mm @ f/4 the lens shows very noticeable vignetting (~1.4EV) which will be visible in most scenes. At f/5.6 the problem is already largely reduced (~0.78EV) but stopping down a little further may be a good idea if required. At 18mm and 24mm vignetting is far less pronounced even at wide-open aperture. One stop down vignetting is already quite negligible here.
Similar to the distortion characteristic vignetting is again more intense on the D200 (1.5x crop) vs the EOS 350D (1.6x).