By the time Belshazzar starts messing with the wrong sacred vessels—which is right away—we know that he's getting ready for a pretty big tumble. Belshazzar is like a B-Side Nebuchadnezzar. He has all of his grandfather's (Nebby's) bad qualities, but none of the good ones.
And Belshazzar doesn't just mess with the wrong cups—he messes with God's cups. And God, as it turns out, is a little more than protective of his cups.
God does not appreciate Babylonian kings holding crazy parties and letting everyone drink Mountain Dew: Code Red (or whatever other unholy beverages they drink at these festivities) out of vessels dedicated to him in Jerusalem. When Belshazzar says, "Hey, let's put away these promotional Dark Knight Returns glasses, and start using these really cool holy ones," we want to scream at the page, "Stop, idiot!" But he doesn't stop. And we know what's coming.
After Belshazzar sees the "writing on the wall"—which a mysterious disappearing hand puts there—he realizes this mad foray with the cups was a bad idea. His smart queen suggests that he call on Daniel (he should have done it sooner, following his grand-dad's example), but it's too late. Daniel's like, "Sorry, Bro—it's over, man. Game over. Just—Game Over." Somehow, this gets Daniel another promotion. But Belshazzar gets destroyed and Darius the Mede takes over later that night. Yeah—that was fast. But God loved those cups.
What makes Belshazzar so bad and thick? He's got all the pride of a typical Babylonian king, but none of the latent capacity for spirituality and humility that Nebuchadnezzar had. And if you can't recognize God's kingdom as being above your kingdom—and you're going to have some sort of crazy chug-a-mug session with God's own special cups—hey, that's it. We'll say it again: game over. He should've already been able to feel the graveyard dirt falling over his head.