If there is a weakness then it seems to be in the way you describe it, rather than the idea itself. I'm really not that good at General Relativity, or at least the maths of it, but in a nutshell you can imagine that the Universe does exist at at once, from a certain point of view, and so that all of time exists "simultaneously". Loosely you can imagine of time as one axis of a graph of the universe, and then the graph itself can exist all at once while the Universe develops in that graph; or perhaps, it's like a movie-reel that can only be played a frame at a time, but still exists completely.
Then you can start drawing routes which objects and individuals can take through space and time, and there are several well-known cases in which these loop back on themselves -- a "closed timelike curve", which means that you arrive back at where you started both in space and in time. It's not unreasonable to imagine that these loops might also latch on to a forward-moving line, so that something moving along this line could take a journey forwards, loop back on itself, and move forwards again. Why could they not pick up memories along the way that they would suddenly experience all at once, and so see the future?
So much for allowing that your idea is plausible, and at some level already exists. There are however problems with the idea. In order to get these effects gravity needs to be locally very strong, so what is going on at the surface of the Earth shouldn't be enough to bend time back on itself. Secondly, if such loops existed and could be seen (it's reckoned, for example, that such weird stuff goes on behind the event horizons of Black Holes, and are therefore cut off from the rest of the Universe) -- if these weird loops could be seen, then, they would essentially destroy the predictive power of classical physics. This is not necessarily a strong argument against the idea, but naturally physicists would rather that we could make predictions about the future. This is difficult if the future influences the past, and we need that past to predict things. At any rate, Causality -- "events can only be influenced by that which precedes them" -- is pretty well essential to Physics and all of Science and it isn't going to be got rid of lightly.
What this means is that the idea of a "flaw" emerging is, I think, possible, but probably not on Earth. Odd, that, but there you go. I think you might enjoy reading more about General Relativity, as the nature of time in GR as I understand it is not all that different from your idea.