> a worse problem than the one we started with

Bacterial infections are no longer a serious threat -- even bubonic plague has been brought under control. It's unlikely that bacteria will ever become fully immune to one or another antibiotic, but if that does happen we've still got penicillin, bacteriophages, and sterilization techniques; bacteria will never again be as dangerous as they were as recently as the late 1800s.

For further clear-cut changes of the world for the better, there's smallpox eradication, the immanent eradication of guinea worms, the extirpation of polio from most of the world, and the development of anaesthesia.