Overall, you’ve raised some very good points about problems of determinism and predictability even in classical physics. However, to get back to the original question of teleology: first, it seems to me that even if there are cases in classical physics (space invaders, Norton’s dome, etc.) which are not predictable, most other situations we encounter in daily life are in principle predictable and deterministic. (Unless you can show me that these problems are also present even in regular phenomena such as heat-seeking missles.)
In contrast, indeterminism seems to be at the heart of quantum mechanics, such that literally nothing is 100% determined.
In any case, going back to @EricMH’s definition of teleology:
In the case of classical mechanics, most things have P(X)=1 (as in the Laplace demon picture of the world), except for the predictability edge cases listed by @PdotdQ. Thus, according to this definition, most things are intrinsically teleological.
In the case of quantum mechanics, nothing has P(X) = 1. Thus, nothing is teleological. And as @PdotdQ pointed out, this touches every model of the universe which includes QM, including QFT, quantum gravity and combination of that.
So, @EricMH’s definition of intrinsic teleology is either trivial (as it applies to most objects), or inapplicable (as it applies to no objects). In either case, it seems the definition is flawed.