Being quite familiar with Scripture I can't think of anything in Scripture which should be contradictory to the theory of common descent. The only way I can see this being the case is by insisting that the creation narratives of Genesis 1 & 2 are to be taken literally, and I've already provided one major reason why they shouldn't. There are two creation stories, right next to each other, and if they are taken literally then they are irreconcilably different--and attempts at trying to reconcile them usually amounts to nothing more than adding to the text or engaging in massive eisegesis.
The creation narratives aren't there to give us a scientific-like explanation of material (or human) origins; they are there to communicate important points of theology which become increasingly relevant as the biblical narrative continues. And, if we are Christians, we understand that narrative as reaching its climax in the person of Jesus Christ. Origen makes a pretty solid point when he writes,
"For who that has understanding will suppose that the first, and second, and third day, and the evening and the morning, existed without a sun, and moon, and stars? And that the first day was, as it were, also without a sky? And who is so foolish as to suppose that God, after the manner of a husbandman, planted a paradise in Eden, towards the east, and placed in it a tree of life, visible and palpable, so that one tasting of the fruit by the bodily teeth obtained life? And again, that one was a partaker of good and evil by masticating what was taken from the tree? And if God is said to walk in the paradise in the evening, and Adam to hide himself under a tree, I do not suppose that anyone doubts that these things figuratively indicate certain mysteries, the history having taken place in appearance, and not literally." - Origen of Alexandria, De Principiis, Book IV, ch. 16
-CryptoLutheran