Is Baron and Kenny method for mediation now outdated? This is because I got a comment from reviewer saying asking me to refer to Rucker, D.D., Preacher, K.J., Tormala, Z.L. & Petty, R.E. (2011). Mediation analysis in social psychology: Current practices and new recommendations.
Baron and Kenny are indeed outdated, though that does not make them wrong in all cases.
The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference your reviewer suggests and in the literature alluded to by @PeterFlom, and broadly non-statistical concerns about the definition and causal identification of mediation effects.
Following this order it might be helpful to start your reading with MacKinnon et al.'s 2007 review, or with the reviewers suggested reading. Then move on to Imai et al. 2010a (or Imai et al. 2010b) These last papers are dense, but repay study. that should bring you more or less up to speed on how mediation analysis is being thought of lately.
This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, so my comments may not apply to everything). It may also relate to the 2011 paper you mention, which I have only had the chance to skim through just now.
From what I've seen, the idea of measuring/establishing mediation mostly seems to suffer a basic problem* that I haven't seen adequately dealt with. (I've just taken a fairly quick look at the 2011 paper you mention, so maybe I missed something. The example in figure 2 of the paper seems to be related, which is encouraging in the sense that at least some possibilities are being mentioned in some parts of the literature now.)
* The first time I ever heard of mediation and read a copy of Baron & Kenny, I saw this would be an issue. It seemed to be a surprise to most people I mentioned it to.
The problem is this - to establish that $M$ actually mediates $X\to Y$ (at least partly), as below:
(the dashed arrow indicates a reduced level of relationship), it is necessary (for example) to rule out all feasible explanations like these in place of the second diagram:
(The grey variables might be latent, unknown, unaccounted for - or in some other sense 'hidden' from the model, or the researcher, or perhaps even anyone. There may also be some direct relationship between $X$ and $Y$ as well, it makes no real difference to this issue.)
Many papers (at least many of the ones I have seen) which deal with mediation, when they follow the recipe that is supposed to establish whether mediation happens, immediately start saying things along the lines of "$M$ mediates $X\to Y$" and discuss the size of this effect, when unless they have eliminated essentially any possibility of such hidden variables actually driving the relationship in any number of arrangements and variations, they really haven't established such a thing at all, and any measures of the size of the mediation effect rely heavily on those other possibilities not being present, at least not to any substantive degree.
An additional issue is that methods such as regression don't "put heads on arrows". To do so with such methods requires careful experiments, or very careful argument; if both are missing, generally speaking all really we have is correlation, and correlation is not the same thing as causation.
I am hoping one of the very good quality statisticians here will be able to school me on why my concerns are mostly unfounded; such an education would be most welcome.
Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuum. This makes more sense to me.