The FDA (and to a lesser extent regulatory agencies generally) being extremely over-reluctant to approve things, because of the misaligned incentive that heavily punishes approving something that ends up being bad, but doesn't generally punish failing to approve something that would have been good. For the greater public good, individuals within the organization would have to take on substantially more personal risk, with little to no corresponding personal gain.
Much lumber and other treated wood is treated with formaldehyde, a carcinogen, which then vaporizes back out of the wood over time, causing a health risk. The EPA regulates the allowed quantity of formaldehyde emission, but the limits, while they prevent acute poisoning, leave a substantial carcinogenic effect. The costs (an increased level of cancer in some people, likely dozens of years later) are diffuse and hard to notice, so there is no great incentive for the EPA to reduce the requirement, and formaldehyde is a useful treatment, so the companies themselves have no incentive to unilaterally reduce their use of formaldehyde. Thus, people who work with wood and those in newly constructed wooden structures bear an increased risk of cancer.
Schools starting at times much earlier than the window of wakefulness for teenagers. It's likely that the knowledge diffusion problem has some impact (I do not have good information about how many school administrators don't know the science, vs how many are just ignoring it), but even with appropriate knowledge diffusion, a degree of incentive misalignment remains, where the people who suffer the most (the students) have nearly no power to enact the policies, while the adult administrators, with their earlier circadian rhythm, bear no personal cost from the schedule. Likely the combination of both leads to the current state of affairs persisting, as there is some incentive for the administrators to use better schedules, as students would be able to perform better on tests when properly awake.
Ongoing overfishing of ocean fish. Each individual fishery (and, at a higher level, each country) would prefer a world where everyone fishes a sustainable amount, rather than overfishing and crashing the fish populations that they all rely upon, but without a centralized enforcement mechanism, they have no way of ensuring that the other fisheries (or countries) go along with them in cutting back on fishing, so unilaterally doing so would simply make them get out-competed by others.
The lemon problem. Someone is selling their used car, and they know that it works fine, but they have no real way to cheaply, credibly give that information to prospective buyers. Pretty much any assurances that the seller could give the buyer could also be given by someone with a lemon, as long as that lemon works at least some of the time, so the information can't reliably propagate, and the used-car market remain inefficient, with the uncertainty effectively being a tax on all transactions.
Countries building up their militaries. Most of the use of sizable militiaries is fighting against other militaries (and as a deterrent against such), so they are overall a negative-sum game. If countries all agreed to cut back their militaries, they would (for the most part) all benefit, but due to the competitive nature, there is a strong incentive to not cut back. Even if a cutting-back deal were arranged, there would be a strong incentive to merely produce the appearance of cutting back, while maintaining as much capacity as possible, as doing so would lead to an advantage against their newly-weakened rivals. Thus, the combination of the multipolar nature (hindering cooperation in the first place) and the difficulty of credibly demilitarizing puts an upward pressure on military expenditure.
The "race to the bottom" problem. Using companies producing widgets as an example, each company might wish to fairly pay their workers, maintain a safe work environment, and not pollute the environment. However, other companies can gain an edge by sacrificing things in favor of producing more widgets (e.g. hiring more workers at cheaper wages). Thus, the principled company must make similar changes, or get outcompeted. This can continue until the companies have all sacrificed everything they can in favor of more productivity, even if all of them would have preferred to peacefully coexist with comfortable work conditions.
Doctors being overly cautious in treatment. Similarly to the first example, the incentives punish positive mistakes much more heavily than negative ones. In this case, any deviation from what is considered to be the "proper" way of dealing with a case subjects the doctor to risk of being sued for malpractice in a way that sticking to the "proper" method does not, even if the deviation would have been a net positive in expectation for the patient. On a similar note, severe problems as a result of treatment gain much more than proportional negative attention relative to minor problems, so doctors have an incentive to avoid even small chances of severe negative results, in the process causing much larger amounts of harm to patients through large amounts of small harms (e.g., the doctor's more at risk if one patient gets a stroke than if a thousand get headaches).

EDIT: For some of these, the end-state is not especially stable by itself. In those cases, central enforcement would likely be the most realistic way to stabilize it.

Market Inefficiency

Market Inefficiency