I'm baffled by this. I mean anything can be dangerous. What specifically is considered the danger with cisterns?

Regarding an overflow, it just depends on your system. Some cisterns have an overflow, and some just fill until full and then anything more will just run off.

As for a cistern becoming contaminated by bacteria and so on it will depend on how well you take care of it, just like a pool. However, pools are much harder to take care of due to the generally large surface area and because they're open to the environment.

Rainwater is a relatively clean source of water, depending of course on your location so most of the initial worries will come from the contaminants it encounters on the way to the cistern. For example, if you have a lot of pigeons on your rooftop, whatever they leave behind is going to be washed into the cistern.

Other types of contaminants and debris such as leaves, twigs, pollen, mold spores and so on can be avoided by diverting the first rains away from the cistern and then using screens and simple inlet filters. Still, something is bound to get through.

A secondary concern for contamination will be contamination of the cistern itself. You'll want it to be covered to prevent animals from drinking out of it, defecating and urinating into it, or falling into it and dying. You'll also want it covered well enough to prevent mosquitos from laying eggs in the stored water.

The above should be sufficient for water to be used in just about everything except bathing and consumption.

In the end you'll want a good filter if you're planning to use the water for consumption in the case of an emergency. And as always, chemical treatment or boiling will help as well.

I'm really starting to like some of the UV water treatment elements out there that can be sunk into cisterns and that run on small solar panels.

This is just a few things I've learned about while studying the subject. I could have missed something. If so, please let me know.