One of the bigger difficulties of an old-earth view of the early chapters of Genesis is how to deal with what seems to to be the biblical teaching that death came into the world through sin, since old-earth views usually involve lots of animals dying, eating each other, and even extinction of species long before humans even existed, never mind sinned. David Heddle has some very interesting thoughts on what old-earthers can say about death, some of them entirely new to me.
The most important suggestion is perhaps that death was already around before the human fall because of the earlier angelic fall, but this was not death for humans. That's what made Eden special. What separates Eden from the rest of the world on the young-earth view? If there's no good answer to that (and there are some answers in the comments, but nothing as huge as death), then this problem, originally against old-earth views, one of the few that I consider serious enough to worry about) actually favors old-earth views on one score rather than undermining them.