Did "Where the really hard problems are" hold up? What are current ideas on the subject?
Here is a rough summary of the status based on a presentation given by Vardi at a Workshop on Finite and Algorithmic Model Theory (2012):

It was observed that hard instances lie at the phase transition from under- to over-constrained region. The fundamental conjecture is that there is strong connection between phase-transitions and computational complexity of NP problems. 

Achlioptas–Coja-Oghlan, found that there is a density in the satisfiabe region
where the solution space shatters into exponentially many small clusters. Vinay Deolalikar based his famous attempt to proof $P \ne NP$ on the assumption that shattering implies computational hardness. Deolalikar’s Proof was refuted by the fact that XOR-SAT is in $P$ and it shatters. Therefore, shattering can not be used to prove computational hardness.

The current mainstream thinking seems to be (as stated by Vardi) that phase-transitions are not intrinsically connected to computational complexity. 

Finally, Here is an article published in Nature which investigates the connection between phase-transitions and computational hardness of K-SAT.