I would start with Genesis. The very creation story with plants being created before the sun simply goes against the way things work. I suppose they could have been without light for the day or two it took before god actually got around to creating the sun, though, on the other hand there was the "light" which was created prior to everything else.
What was that, though? Some sort of cosmic shop-light? Or does that mean that people of those days simply believed that daytime was light and nighttime dark, and the sun and moon were only ornaments in the sky? That is rather the way the story reads.
There are many other things, such as breeding goats in front of striped sticks to get striped goats (or whatever exactly that verse is, sorry, don't have the ambition to look it up, but it gets mentioned so often that I don't think I need to). But when there is such a glaring anomaly right in the first couple of sentences, I think there is the natural tendency, in this more enlightened age, to take the whole thing as mythology.