Vignetting ....

...can actually get worse the faster a lens is.

I have the Canon 85mm F1.2 II. It is great at F1.2, but the edges of photos are quite dark (when used on a full -frame body). Stop it down to F3 and the vignetting is totally gone.

The size of the objective is one of the critical factors affecting vignetting. It's like having an inappropriately sized lens hood, but very out of focus (as you might imagine for a fast lens).

Fast lenses generally are sharper where telescopic resolving power is needed (which does not apply to this camera). The effects of diffraction (blurring) at the telephoto end for compact hyperzoom (> x20) cameras are testament to that.

For this camera, the limited wideangle/telephoto range and small imager may render vignetting insignificant.

However, vignetting can actually be beneficial...

further to what Ball Boy wrote...

the 'faster' the lens the larger the aperture, i.e. more light getting in, hence faster AF (if it goes through the lens) and shorter shutter times. a larger aperture also means a narrower depth of field, which makes everything that is not focused blurred ('background defocus' as the TV ads say). A smaller aperture means a larger depth of field, which makes everything in the frame sharper. Neither of these is better than the other. It's up to the photographer which he wants to use. Though a narrow depth of field is generally harder to work with.

Hence to get a sharper image on a wider aperture, you're actually relying on the quality of the optics.

Bring back the blue door! And I miss the cathedral.