Nikkor 16-35 f4: is that bad in corners?

It can be but it sort of depends on how you use it. It's more useful than the 14-24 but the 14-24 is optically a lot better.

That said I think the 16-35 has it over the 14-24 for sharpness but not so much that you would ditch the 14-24.

I actually started out with the 16-35 and then returned it for a 14-24 but now I kind of miss the 16-35 and am thinking of buying it back.

Anyway, I did a Blog post  on the 16-35 with samples and such, it may help you make up your mind.

--
http://stevejwphotography.blogspot.com.au/
http://www.flickr.com/photos/stevejwphoto/