Based on the fact that it's allowed in Islam, I never had anything against it. In fact, I know quite a few families where they've practiced first cousin marriages sometimes over more than a single generation (i.e. their parents are first cousins, and then the children of those parents once again married their first cousins). Their children are fine, Alhamdulillah.
Whenever I've heard/seen people being worried about children from cousin marriages, it's almost always seemed to me that they're exaggerating the risk. I've studied genetics in biology class, and I know the principle of having recessive genes become more common after generations of cousin marriages but when done in one or two consecutive generations, I wouldn't worry about it too much.
As far as the social aspect, it really doesn't bother me. I see a couple consisting of cousins to be just as legitimate as a couple consisting of otherwise unrelated man and wife.