Rav Heinemann said that if the DNA of something does not affect the taste (or smell, sound, appearance) of it, then the fact that the DNA is present does not make a difference. He explained this as a function of the same principle that allows us to eat bacteria - halacha deals with what you can detect (even though we could use a microscope to see it. The Torah deals with the realm of our natural experience). If the tomato has no characteristics that observably resemble the pig that the DNA came from, then it is OK. However, if it does have observable features that liken it to its DNA source, it is a problem (an oinking tomato would not be Kosher).
Additionally, a friend pointed out that most genetic engineering and modification is not actually done with DNA directly from the organism that provided the DNA, but rather they synthetically copy the DNA (is is a much more efficient way to produce a lot of it) and then inject that into the specimen. Rav Heinemann said that if that is the case, then it isn't considered as being non-Kosher DNA in the first place - it is a synthetic replica, but not the actual non-Kosher species. Therefore, even if it gave taste, it wouldn't matter.