When this was selected I jumped it to the top of my "to read" list". I am now half way through it, slowly as am fitting it in among other things, so, at this stage, I will just comment on initial reading impressions rather than messages that I think may be buried in it.
I don't read much science fiction, although I do generally enjoy it. Has really just been one or two, spread over many years, from each of the likes of Clarke, Asimov (but more of his such as Robot and Foundation series), Heinlein, Herbert, etc. as well as the older classics from Verne, Wells, Stevenson, etc. Also I never read short stories as they often strike me as being frivolous and reminding me of the terrible days of glorified school essays (I enjoy good novellas though) so to approach a book which is basically a collection of short stories within a quite tenuous frame and a genre I don't often read was not attractive. For Bradbury I had read only
Fahrenheit 451 years ago and recall that while I liked it, that was not enough to prioritise his other books for my reading over those from other authors.
But I am glad I started
'Chronicles and am enjoying it - I am reading the 1997 version.
For the first "short stories" which are (in my view) hardly related at all, I thought the book was going to be a mission to read but as I got further into it they became retrospectively framed. And my aversion to short stories was overcome, I think because they represent a (fictional) history and history is just one big story made up of many collections of both closely and loosely related short stories, and I can read history no problem at all.
For science fiction I have never let lack of technical accuracy get in the way of enjoying it (despite physics being one of my university majors) so the fact that we now know there is no advanced life on Mars does not detract and, as another Mars example, the likes of
The War of the Worlds is for me an enjoyable read.
The same applies to the date thing, I would not have had any qualms reading the original version with the now past time-line, just as I have no problem reading
2001: A Space Odyssey. Perhaps I am easy on this because there is important philosophical and theoretical pondering in physics over what time is actually, and the conflicts regarding that between classical, relativistic and quantum physics. In the end, if nothing else, I find it interesting to see how those in the past foresaw the future we are now in panning out insofar as it could provide a frame for their story.
There is quite a lot of figurative prose in the stories (FantasyFan has mentioned "Ylla", for example) and I like the way that where that is cryptic it is not ambiguous (cryptic prose that is ambiguous I regard, for myself, as a serious turn off and even a fault e.g. such as in
Mrs. Dalloway 
). I think the narration is well done for the loose storyline, I am not sure why at this stage but perhaps because of the way that it changes its focus from time to time?