I can only see one potential problem with interracial dating. That is the potential of disobeying a scriptural instruction.
2Corinthians
(6:14) Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
(6:15) And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?
(6:16) And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
We are clearly told to not enter into a relationship with those who are not believers. So here is the potential problem. Not because of their race, but because of what that racial back ground may have taught them to believe.
I find it interesting that I can not bring to mind a case in the Bible where, the reason the examples being told their relationship was wrong, that race was the issue. It was not that they were racially different, they were spiritually different.
The example of the ox and the ass being yoked together is the reason behind the belief that interracial relationships are wrong. We need to keep in mind that image this creates for us is almost extreme in its illustration. Yet if we look closely it is not the physical differences in this combination that are explained. It is the behavioral differences.
Different races believe different. This is simply due to different geographical origins. Those origins separated by distance will develope different beliefs. It is those beliefs that can be the danger in any relationship.
Our oldest daughter is very attracted to the males of another race. We often have conversations due to this attraction. In her case though it has yet to develope beyond the friendship stage. This is due to the fact that as she says " they just don't believe the way I do". She recognizes the danger. Not because of the color of their skin. But the condition of their heart.