Tough question!
I'd outright reject the areas that are obviously false, I'd also seriously question the validity of the rest of the scripture too. I don't think I'd take many parts of the bible seriously at their face value, but I don't think it's all 100% BS. The bible has some great values, but it also has so many archaic/outdated/simply retarded ones.
I'm not a historian but I think I'm right in saying that they examine each aspect to determine its validity and if something isn't valid they will reject that part.
I can certainly see why there is debate around the reliability of scripture but it is all dependent on the interpretation.
I won't expect an atheist to believe it is an inspired book but at the same time it still has to be examined like any other ancient text.