As far as the media talking about any players - not just keepers - they exaggerate the situation. For them, a player is either completely useless or a god. The idea that a player can generally be very good but make some mistakes now and then does not seem to be a concept they can deal with. So what they think of Hart, Reina or anyone else does not really interest me.
Back to keepers saving. The fact is that in order to stop a shot when the opponent gets in closer, the keeper - like during a pelanty - basically has to guess which way it is going. Even if he leaves the final decision late, he will be mentally getting ready to dive one way or the other, so he can be wrong-footed before he then moves. It can look as if he has just reacted late whereas it is just him changing balance - something not easy to spot.
When a keeper is, for instance, 'beaten at the near post' which all the punters say is something that should never happen - that is not realistic. If you watch most strikers, when they are coming in at an angle will more often than not - by a big margin - shoot for the far post. If you are a keeper, you will likely position yourself to discourage a shot to the near post and tense your muscles ready to spring to cover a shot to the far post. If a striker then unexpectedly shoots for the near post, a keeper - even a really good one - can be beaten if the shot is fast enough.
Again, the commentators take a real bias here. They decide on a great shot or save on whether the players involved are in the list of 'great/favoured' players or not. A ball can be deflected from a Rooney shot that was going wide and that is still a great shot. If it is a championship player making the same shot, it is a lucky deflection. Of course if a keeper is hit by a shot from point blank range when he was simply standing there, then if he is a favoured player it is a great save. etc.