First of all, nobody's mentioned the Heisenburg Uncertainty Principle or the Planck-sized limit to accurate observation. i.e. after a while, observing/measuring the system in a classic sense is going to only get so much information out (e.g. position
or velocity of particle, not both), and is going to knock the quantum state around while you're doing so, thus invalidating your results. All the while leaving 'unknown details' in the mix.
So a universe which is deterministic might still be incalculable. Which is not to say that a simulation can't be sufficiently detailed to provide a reasonably accurate prediction. But tend towards believing that Butterfly Effects (minor differences, not taken account of or fudged over, between two possible starting states on any simulation) are the deal-breaker and the implied randomness of result or superposition effects of the quantum world are artifacts of us not able to know the precise rules or configuration of the sub-Planck world underlying that which we can measure to a certain macroscopic certainty.
(Not the reference to that being my belief. That form of fatalism is probably as close as I come to a practical religion.
Regarding predictions affecting a system, I have been known to refer to self-fulfilling prophecies in the style of Macbeth. Had the witches not informed the Scottish Lord himself of his destiny, would he (and his wife) have pursued the course of actions that sent him towards the fate that awaited him? Had they not given him reassurance that only certain obviously ridiculous circumstances could harm him, would he have remained as unconcerned about events until the predictions took place?
Usually I apply the above to philosophical discussions about time-travel scenarios. Universes that contain closed time-like curves (yes, this time it is time-like that I mean
that do not have splintering/branching or other interesting variations on alternate futures must be self-consistent in that "everything that you go back and do, you must have already been back and done", which includes the situation where 'predictions' you make (or warnings) by using information from the future must support the creation of the timeline where this happened. In fiction, this is usually because of unforeseen interpretations meaning that (in this particular type of unalterable time-line universe) attempts to make changes are the inadvertent cause of the things one wanted to change (or, at the very least, fail disastrously). The average film-goer can name numerous films that have such self-supporting feedback loops in them, so I won't bore you with a list. Sometime's it's put down to the Universe "conspiring against" the change, as with the "History will out" types (details change, but the overall run of the game stays the same).
Different uillustrative examples would be the 'new branch creation' types, with the Terminator series as one prime example[1]. At the end of my (unofficial) list of types, there's the Back To The Future types, with Flip-Flop universes and 'fading from reality' effects when things are
about to go irreversibly wrong, which then give impetus to your efforts to correct things and allow you to fade back in.
(Illustrative examples only.)
[1] If you don't believe that the information about the timing of Judgement Day might have been deliberately miscommunicated to the past by those sent/sending back to the past... Not sure if the Sarah Connor Chronicles have anything to add to this argument.