David Preece, who is a goalkeeping coach who occasionally does the rounds on the podcasts, media said that Hart's problems were/are pretty much all to do with his work ethic.
As Preece tells it, Joe came through with Massimo Battara, Mancini's goalkeeping coach, who used to really crack the whip and force him to spend a lot of time working on the weak parts of his game. Battara was like Mancini a strict old-school italian coach and Joe being a nobody when he first met him was very much done what he was told, and the two of them were very successful in turning Hart into the keeper he was around 2011-2013.
When Battara left and our current coach, Xabi Mancisidor came in, Hart was the starting keeper with titles under his belt and England #1 and pretty much decided he could dictate what he worked on in training and started ignoring the weak areas of his game and parts of training he didn't like but was forced to do under the stricter Battara.
And this pretty much lead to him being the player he was after that - making lots of great reflex saves, but also loads of blunders.
I think as fans we under-reacted at the time to the fact Pellegrini dropped him twice for complacency. Looking back, what other top keepers get dropped like that? No one.