Open Question: Can genetic engineering & modification have unforeseen negative consequences in the long run?

I'm not really a "science" person, and am not up on all of the debates, but I see, hear, and read stuff about rodents and livestock being modified with genes from humans and other stuff going on with transgenesis and various types of hybridization, and it gets me to thinking about a bunch of admittedly far-fetched scenarios, and I get worried...
I think about the potential offspring of these animals, even the ones in labs who aren't meant to reproduce, but who somehow might still be able to,

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