Disinfect the pot thoroughly between uses, and always use distilled or boiled water!
I'll be honest with you, even before this story broke, there was no way on this green Earth I was ever going to use a neti pot. Actually I shouldn't say that, because I never like to say "never." So let's just say that "it would take a lot" for me to use a neti pot. Like a gun to my head, or a life-threatening illness that can literally only be cured by pouring warm water into one nostril and letting it run out the other nostril.
The brain-eating amoeba is an interesting creature known as Naeglaria fowleri, which kills several people every year. The typical N. fowleri infection comes from warm, stagnant lake water, which is why it is a particular hazard in the Southern U.S. during the late summer and early fall.
This organism enters the body through the nose, as when you jump into a pond and some water gets up your nose. It swims up your sinuses, attaches itself to your olfactory nerves, and uses those to hike their way to the brain. Once in the brain it sets up shop - with fatal results.
N. fowleri is surprisingly fatal, with only about 3% of its victims surviving the attack. This is partly because many people are not taken to the ER until it is too late, since the earliest symptoms of a N. fowleri infection are very similar to a bad cold or the flu: headaches, vomiting, stiff joints, and a sore neck.
Unfortunately, it now seems that N. fowleri can sometimes be found inside the home. This is particularly the case again in the Southern U.S. where a quirk of the pipes may result in a stagnant area of water where the organisms can flourish. In the case of a man who died in Louisiana, health officials found the organism in his home's water, but not in the municipal water supplies. Could it be lurking in his hot water heater, or in an outdoor pipe? Uncertain.
Most of the time, even if you have N. fowleri in your home's water supply, it isn't going to be an issue. Water has to be forced pretty far up your nose in order for the organism to reach your sinuses and then your olfactory nerves. Taking a shower, even taking a bath and submerging your face is probably still safe. But pour water into your sinuses with a neti pot, and you could be in trouble.
If you do choose to a neti pot, be sure to follow the manufacturer's recommendations. Disinfect the pot thoroughly between uses, and always use distilled or boiled water, never just warm water straight from the tap.