I’ll certainly give you his hamfisted attempts at romance - across all his books, it rarely works.
I would (personally) disagree with the ‘societal’ development piece. In historical fiction, it is often a device that characters within a book achieve technological/societal advances or changes that would have occurred gradually through many people - it gives the reader at least a picture of the changes that were happening while having some investment in the results of those changes. Sometimes it works better than others - I don’t remember Pillars of the Earth being particularly egregious in this manner, although it has been a while since I read it.
Personally I enjoyed the heel/face stuff - simplistic in some cases, but very satisfying in others.
Conn Iggulden, as far as I can tell, is more widely regarded as a writer of great rip-roaring novels than being historically accurate - if you want historical accurate (and I believe Ken Follett, apart from one or two minor examples, like having lowly characters eat breakfast at a time when they probably wouldn’t have eaten anything until the main meal of the day) I’d look for Sharon Penman, Colleen McCullough or Harry Sidebottom