Can't we leave well enough alone?

I was reading an article in The Onion May 16th 2001 “New Technological Breakthrough To Fix Problems of Previous Breakthrough”. Even though this article is completely satire, one paragraph in this article really got my attention. It relates to the hydrogen bomb and the supposed breakthroughs in science it brought about.
“Not only was it a tremendous breakthrough in physics, it broadened our knowledge of everything from radiation containment to bomb shelter construction to hair loss”. Contemplating the irony I asked myself, “Why can’t we leave well enough alone”? Striving for a better tomorrow is the assumption most people have regarding science and its breakthroughs in technology. But with every right turn we have made, there are hundreds of mistakes that no one knows about or cares to tell.
Take the honeybee for example; in 1956 someone had a brilliant idea to crossbreed European honeybees with African honeybees in an effort to increase honey production. One problem, the bees escaped to form a hybrid colony of feral bees that infested other colonies and produced less honey than the native species. One day, North and South America will be infested with these non-native species, possibly crippling the "honey economy" and wiping out our "good" pollinating friends. Even with something so apparently trivial as honeybees, we can’t get out of our own way. I know you would be hard pressed to find anyone whom could have predicted such dramatic results. But as some point, can’t we just leave well enough alone?
Pushing the envelope is what has sparked positive innovation in so many important fields and I get that. But is there not a cause for concern that our innovation has done more harm than good? Have we advanced to far to soon? Do we fully understand our scientific actions and the repercussions that can happen? I am not an advocate for a return to the Stone Age; I am just a student asking a question.
Can we?