Whether self-organized criticality needs hidden fine tuning
In plain words
Sandpile models reach criticality by themselves only when grains are added infinitely slowly and lost only at the edges, which are tuned limits in disguise. Whether any natural system shows criticality without such hidden tuning is unresolved.
Precise statement
Determine whether physically realizable driven dissipative systems exist whose steady state is critical (avalanche distributions with a cutoff diverging with system size) for an open set of control parameters, as opposed to requiring the double limit of drive rate $h \to 0$ and bulk dissipation $\epsilon \to 0$ that maps self-organized criticality onto a tuned absorbing-state transition. Answer: yes with a model or experiment, or no with a general argument.
What would settle it
A model or experiment showing size-divergent avalanche cutoffs over a finite range of drive and dissipation rates, or a proof that the double limit is necessary for a stated class.