I agree 100% with Sabine Hossenfelder's list of what are and are not "good problems" in fundamental physics in a recent post at Backreaction.
In short: inconsistencies between accepted theories or between accepted theories and observation are problems, while dissatisfaction with the form of the laws of Nature that have been experimentally discerned are not.
I would add that it isn't inherently wrong to look for more elegant ways to describe existing descriptions of the laws of Nature that are not inconsistent with observation or other physical laws, but that this doesn't make them "problems" that need to be solved by physicists. (In the same way, even tough there is more than one way to prove the Pythagorean Theorem, the validity of the Pythagorean Theorem ceased to be a "problem" once it was first proven, even though not every means of proving it had been articulated at that point.)
I also agree that her placement of the phenomena associated with "dark matter" at the top of her list of "good problems" is appropriate. The existence of these phenomena are established by overwhelming evidence and they can only be explained with "new physics" or (at least) a major reinterpretation of existing physics as it is applied today. Further, figuring out the cause of "dark matter phenomena" is likely to have applications that are predictive, in addition to explaining existing knowledge.