Stars that are more than 4,000 light-years away.

[exercise in ridiculous logic]
Just to point this out, saying that light is only just now reaching us that would have been generated 4,000 years ago if generated by the star doesn't mean the earth is 4,000 years old, or even that the universe is that old. Granted, it is HIGHLY likely (%99.9999), but the moment you stipulate that God can create everything in the blink of an eye, you also must admit he can put anything into motion he wants, including energy emissions that are already in progress. If the purpose of starlight was to demonstrate the vastness of the heavens to human beings rather than as a scientific measure of how long stars have been around, that could even make sense.

To think of it in a different light, in the New Testament it is recorded that Jesus made fish appear (apparently) out of thin air. If a scientist had gotten hold of one of these fish he would have concluded that the fish had lived, been caught, gutted by a fisherman, and other things based on solid scientific observation. But he would have been wrong because he made (normally very correct) assumptions about the way the world works. And I don't think this would be construed as "God lying"; the purpose of the fish was to feed people, not give them a lesson about the life of a fish. The same could be true for starlight (though I doubt it).

Of course, scientifically we cannot adopt that kind of reasoning because it would make scientific assumptions meaningless. But I would have to say that any point we're talking about God interfering in the natural order of things science will not be able to adequately explain it because science is based on reproducible and rational behavior.

The whole point of this post is to say we really don't know anything, but we have some very rational and solid ideas. But concerning creation we all have to admit that there is some sense of ambiguity. There's just too much we don't know. Even the Christian who believes that "God did it," still has a lot of unanswered questions.
[/exercise in ridiculous logic]

Note: this is not my view on creation at all. I believe God did it and he created humans as His special creation. Beyond that I know/believe very little. And I think the bible is consistent with "old earth" evidence.