There is a song, "Beautiful Scandalous Night." Also, I have heard this term used with regards to the crucifixion. I assume this does not have the colloquial meaning. What does it mean?
Perhaps the closest biblical connection is to 1 Corinthians 1:23:
we preach Christ crucified, a stumbling block to Jews and folly to Gentiles (ESV)
Ravi Zacharias makes this connection in an article entitled "The Scandal of the Cross":
To the Greek, the cross was foolishness. To the Jew, it was a stumbling block. What is it about the cross of Christ that so roundly defies everything that power relishes? Crucifixion was humiliating. It was so humiliating that the Romans who specialized in the art of torture assured their own citizenry that a Roman could never be crucified. But not only was it humiliating, it was excruciating. In fact, the very word “excruciating” comes from two Latin words: ex cruciatus, or out of the cross. Crucifixion was the defining word for pain.
Mark Baker and Joel Green, in Recovering the Scandal of the Cross, also see a connection between this passage and the "scandal" of the crucifixion:
Paul himself provides evidence that we have too easily made sense of the scandal of the death of God's Messiah. In 1 Corinthians 1:18–25, Paul outlines a perspective on the cross many of us have learned to overlook. Here he testifies to the lunacy of the cross for the first-century Roman, matched by its ignominious character among the Jewish people. [...] In Paul's argument with the Corinthians the cross does not have the appearance of "good news" but of absurdity. (33)
And finally, D. A. Carson titles his 2010 book on the crucifixion and resurrection Scandalous, emphasizing the ironies and absurdities associated with the crucifixion (cf. Matthew 27, Romans 3, and Revelation 12). So to many Christian writers, the typical understanding of the word scandalous as "shocking" and "upsetting" (see Merriam-Webster) is perfectly, even eminently, applicable to the cross.