'Good' organic growing practices are perfectly safe. They'll minimize pesticide application, and ensure they do it at the correct times, i.e. away from harvest time. They'll apply Bt toxin (yes, the same stuff in the GMOs, just exogenously applied) and neem oil, as well as some soaps with potassium salts.

There are some 'dangerous' organic pesticides. As far as I know Rotenone isn't used anymore, but it is dangerous to humans and was once employed as an organic pesticide.

Copper sulfate is a fairly big issue. It's definitely toxic to humans and has been found to accumulate in soils. It's a fairly big deal in Napa and the vineyards have moved away from it because of the accumulation. This copper definitely makes it's way to consumers, so the question is how much, and how much is too much?

This is an interesting anecdote about brewing beer with fruit, and needing to pay attention to copper levels. http://scottjanish.com/peaches-and-quinoa-sour/

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Ultimately, at the scale of the modern organic industry, you're not always going to get good stuff. There are certainly potential dangers, just as there are with conventional agriculture. I would contend that both are perfectly safe when done appropriately.