There are a few factual errors here that someone even casually familiar with the event will catch. For instance, the decision to frame the broadcast as a series of news bulletins was part of the idea from the beginning, according to Howard Koch's account of working on the script. The fake-documentary style wasn't adapted only three days before air, as reported here.
What really grated on me, though, were the amateurish recreations of listeners reporting their experiences. These are shot in distressed black and white (like "News On The March" footage), but you know instantly that they're contemporary, over-the-top, rather dinner-theatre-ish performances (with one exception at the end), not remotely convincing as period footage. This is in lamentable contrast to the event being celebrated, in which actors like Frank Readick and Ray Collins really managed to sound like non-actors, to sensational effect.