It looks like a careful bit of work, there's no obvious problem with it, though there is one weakness that the authors are careful to mention, which is that the models may be significantly biased in some way such that an observationally-derived constraint ends in the wrong place. Eg if the models have too much mixing in some other region, or even a bias in some other process or place that compensates, then the Sherwood et al estimate will be biased. A similar issue crops up in the paleo world: if all the simulations of the Last Glacial Maximum use too little negative forcing (which we believe to be the case), then models with the correct intrinsic sensitivity will not be cold enough and a constraint based on LGM temperature change and model simulations will in that case tend to overestimate the true sensitivity.
There's not a whole lot you can do about this problem other than be aware of it, and try to use constraints that are as large scale and relevant to the predictand as possible, to reduce the risk of spurious correlations. That's one reason why I generally prefer the paleo and transient temperature change methods, as despite their own limitations they do at least directly consider the climate response to forcing on large scales. In contrast, emergent constraints generated across the GCM ensemble of climatologies might be spurious (though the ensemble size of Sherwood et al makes this seem a bit unlikely to me) or biased due to other compensating errors. Relatedly, I think I heard a rumour that the previous Fasullo and Trenberth result based on southern ocean biases in CMIP3 disappears in the CMIP5 ensemble. I might have misunderstood this, so don't quote me on it.
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Interesting if the thing about Fasullo and Trenberth is true. A few years ago it was all the rage to talk about a correlation between sensitivity and aerosol forcing in the CMIP3 ensemble. When I looked into the details it became apparent that there was considerable technological stratification in the ensemble: that some models were far more advanced/developed than others. And it turned out, for some reason, that the more advanced ones tended to have higher sensitivities.
The key technology factor for aerosol forcing was whether or not the model included explicit aerosol-cloud interaction. Those that did understandably tended to produce stronger aerosol forcing. And those were almost unanimously at the high-end of sensitivity.
There were also key differences in explicit inclusion of natural aerosol species, like some organic aerosols, dust, sea salt. Since aerosols affect the whole cloud-precipitation system, and therefore relative humidity, presumably a more realistic aerosol implementation would have some effect on the climate process focus of Fasullo and Trenberth.
I have to say I'm way out of my depth on that last suggestion, but, on a general point, from what I know of the CMIP3 ensemble it's entirely plausible to me that their sensitivity correlation was mostly due to this stratification of model complexity in some respect. The CMIP5 ensemble seems mostly to have more equality, complexity-wise.
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