On the subject of the "diamond" planet, I'm actually surprised to see the lead author of the paper in question referring to it as a "diamond planet". I thought that was just a media label. I read the paper when it came out, and all that was indicated was that an extremely large (Jupiter-mass) extremely dense (much smaller than Jupiter) body was detected orbiting a pulsar. The density was consistent with something reasonably close to diamond, but I would have thought that there always has to be some other elements in there... and in any case I wasn't convinced that the vast majority of the interior would be cool enough to be crystalline rather than liquid carbon. So while I'm very confident that there's some extremely massive, extremely dense planet orbiting that star, I'm yet to be one hundred percent convinced that "diamond" is the correct label for it.
Which brings me neatly to the actual point of the article, on climate change. I'm somewhat out of my field here, but no more than the author is. The reason I'm skeptical about the hypothesis "burning fossil fuels is likely to cause significant and disastrous climate change in the future" is that it's all based on simulations which can't be tested against experiment. And I do simulations for a living, so I know enough about them to be very skeptical whenever confronted with simulations in the absence of experiment. Maybe it's true, and I wouldn't be surprised if it were, but I'm certainly not willing to talk about it as if it's as strongly supported as... well, the vast majority of other stuff that we mean when we talk about 'science'.
The strength of a scientific theory is (and I'm still working on figuring out exactly how to phrase this) determined by the question of "If this turned out to be false, how much experimental data would suddenly be very difficult to explain?" If evolution were false, then pretty much all of biology is suddenly very difficult to explain. If the hypothesis "big dense planet thing orbiting PSR J1719−1438" turns out to be false, then there's a bunch of measurements which are very hard to explain. On the other hand if the hypothesis "diamond planet orbiting PSR J1719−1438" is false then it's not at all difficult to explain. And if the hypothesis of significant anthropogenic climate change turns out to be false, then this makes very little difference to our ability to explain existing experimental data.