1. Thematic and ideological concerns that are essentially anachronistic, and the emotionally flat or simply confusing plotting that results from their inclusion.
2. The inadequacy of most Hollywood leading men when faced with the task of playing epic heroes in all their muscular, masculine glory.
3. The failure to embrace the 'otherness' of the past.
In some respects, Douthat has hit the nail on the head. Recent historical epics have been enormous creative as well as commercial disappointments, despite often being placed in the hands of directors who are usually solid at worst (Ridley Scott) or even brilliant (Martin Scorsese, Oliver Stone and Wolfgang Petersen).
Douthat is also absolutely correct to highlight the inadequacy of many of the industry's leading men (most notably the precious Orlando Bloom) when thrust into the role of epic hero. Hollywood is more than ever a temple of youth (or feigned youth), and the boyish charm and charisma of actors like Tom Cruise, Bloom and Colin Farrell are ill-suited to the hypermasculine (and all grown up) gravitas a historical epic typically demands of it male lead (I would, however, quibble with Douthat's backhand dismissal of Brad Pitt's performance as Achilles in Troy, which, by accident or design, perfectly captured the Homeric hero's arrogance, volatility and inhuman detachment and invicibility).
Where Douthat veers off course is in his evaluation of thematic elements and his prescription for revivifying the historical epic as a genre. His contention is that recent period epics have been undermined by the intrusion of modern sensibilities, sensibilities which sabotage what he sees has the primary purpose of the historical epic: providing escapist entertainment through immersion in the spectacle of the past's 'otherness.'
The problems with this approach are twofold. First, it is a reversion to the sort of projective construction of the silent 'other' that forms one of the less admirable subtexts of Western art (the past reimagined as the last colonial frontier). Second, it ignores what made the great period epics of the past so powerfully timeless, namely the ability to address universal or even contemporary questions through the medium of the past. The greatness of films like The Seven Samurai and Aguirre: The Wrath of God is rooted in the way they connect the past with the present, not some alien 'otherness' that allows viewers to escape the moment. Revisionist westerns like Once Upon a Time in the West and Unforgiven owe their success to a similar approach.
The fallacy of Douthat's approach is made abundantly clear by one of the recent historical epics he does praise, Mel Gibson's pornographic snuff flick The Passion of the Christ. Douthat lauds the film for not shying away from the otherness of the past, ignoring the fact that this embrace of the alien past is precisely why The Passion of the Christ was creatively bankrupt: it had no means of reaching anyone who didn't already share Gibson's Dark Age superstitions. Which is why, two years later, despite $350+ million at the box office, The Passion of the Christ is largely a forgotten film.