All I've heard from people that are "skeptical" of the current climate science is that the science is faulty/incomplete/etc. Where is their alternative?
My understanding of science is that it works a lot like the kids' game 'king of the hill.' Whichever hypothesis/model fits the data best is the king, and remains king until either a better hypothesis/model (ie, one that fits the data better) arises or new data comes along that either fits the king so poorly or fits an existing contender better.
Various scientists get ideas for experiments that could knock the king down or help it stay up, others have ideas that could get their contender to the top, and they fight to do just that.
Science is about alternative possibilities. There's the way things are, and there's the way things look. The latter a shadow of the former. It's in our best interest to try to extrapolate from shadow to form, but it's tricky. We go with the best we have for now, and we improve as we continue. If you've got a better idea, let's hear it.
As to particular data that would debunk the anthropogenic hypothesis, that is defined by the hypothesis itself. Data showing the emissions to be smaller than thought, or that the emissions from human activity have some peculiarity that exclude them from significant contribution to the climate, etc. would be necessary to take down the current hypothesis. Data would have to show that man's activities do not significantly contribute to climate.