Suicide rates in Japan is a good start... there's more going on there than just density issues, of course, but they're a good way of pointing out some of the psychological issues related to heavy population density. Psych problems in general are more prevalent in denser areas, as I understand it. Increase the density, logically, you increase the problem -- if not proportionately, then at least in raw numbers.
Many of the lower income or slum areas in the larger US cities are also stuff I'd point to and say, "This is what would be a problem." The issues related to those are tremendous and far from adequately addressed, as well as affecting already tremendous populations. Increasingly sophisticated methodology and technology will help offset that sort of thing, of course! But. The cost is still very, very high.
Then logistic issues... trash disposal, ferex, for larger urbanized areas -- better and more ubiquitous recycling efforts might reduce the problem, but it's still both incredibly non-trivial and something we're not really dealing with. That's far from the only one -- how much arable land does it take to support these places? -- but it's notable and representative. There's a lot needing to be done. Necessity may be the mother of invention, but there is a hell of a lot of invention that needs doing, and even with necessity and genius, it takes time.
High density living is something we've only solved in a sort of engineering sense -- we can build the infrastructure for it, at least as far as the strictly residential requirements go. There's considerably more that needs to be done for that project to really be done. I worry about it, y'know?
Re: Examples: I've been living in Florida for a good long while, now. Most of my immediate experience related to environment related disasters is flood or hurricane related and... in some ways it's incredibly impressive, what we manage. In other ways, well. We've got areas that are scarred several years after the fact, and families that never actually recover from the damage. I see that, and extrapolate. Again, even if the proportion does not change -- even if it gets considerably better! -- the raw numbers would be much, much higher. That's basically what I'm worried about. 99% effectiveness on a global scale is still a death toll of many, many millions. Even if it's better than that, how many decimals back will it go? There's a flat number related to that percentage, and I'm not sure we're going to be capable of getting it low enough to be anything short of horrific. That's basically what worries me, what troubles me at the core.