The Freedman et al. final HKP paper does a good job, IMHO, of laying out the case for the value they conclude with.

Maybe it's worth going over it, and looking at certain sections in some detail?

For example, we could clarify what the +/- numbers refer to (1 sigma? 3 sigma? something else??); the extent to which the secondary methods are independent; dive into the various chains of observations that lead to the stated systematics; consider the importance (or not) of the stated good agreement and consistency; examine the (statistical) approaches to combining different kinds of estimates; and discuss the two quite independent methods (lensing and the SZE).

I think it would also be of considerable interest to compare this paper with the Spergel et al. WMAP 3-year paper ("Implications for Cosmology" - link is to the WMAP site, click on the appropriate link there to get the paper), and the extent to which a value of 84 is consistent with what's reported in this WMAP team paper.