As far as I can see, there are a few glaring plothole errors. First, the Chief was raised on Eridanus (four?) not Mars. Second, how does the Chief teleport from 2552 to 2472 (or perhaps before, as the war between Icarus and Thermopylae happened in 2194). For a moment let's assume that he get's the Jjaro implants. That, however, would require Mjolnir Mk IV parts. I can't see why the UNSC would do that, especially since they wouldn't understand the need, because as far as I can tell, they would have no incentive to downgrade, especially not being aware of the universe-traveling capabilies.
Finally, the Cheif is either seven feet tall or really close to it. Destiny is around 6'6". That's at least five inches difference there. Looks like someone shrunk or grew at some point.
And if Destiny came before the Chief, then explain all of John's childhood.