I'm a bit dubious, since I haven't seen other studies on this topic yet, but I can think of at least one area of significant concern. I've also seen studies linking frankenfoods with leaky gut syndrome, and the whole problem there is that things get out of the digestive system into the body. If we have a food category that increases that tendency, which also contains persistent molecules, that is a very bad combination. Bear in mind that the human body is a lot more agglutinative than most people realize, and not only can new snippets get subsumed into human DNA, they can also latch onto symbiotic organisms necessary for survival and sanity such as gut microbes. So this is something to keep an eye on.
This also makes me wonder if it contributes to the allergies to frankenfoods that Big Food is trying so hard to pretend don't exist. The human body really doesn't like foreign tissue, especially when it gets out of the designated processing zone. If frankenfoods are indeed shedding bits of DNA into the body, I can see why that would make the immune system go haywire. Especially if they really are more prone to do that compared to normal food of similar type.
I'm seeing more and more people complaining of "erratic" allergies where sometimes corn or whatever is fine and other times makes them very sick -- that's either a reaction to different types of corn or to different things put on corn (such as pesticides) that don't appear on labels and thus can't be avoided other than by avoiding the whole category. Some people find that eating only organic food solves their problem, others don't.