Over on his Comedy Central program, Colbert announced that he needed to go to the bathroom, but found that the one in the studio was locked. He then left the studio, telling his audience, "Watch 'Letterman' or something." A few seconds later, he turned up on stage at the Ed Sullivan Theater, interrupting Letterman's monologue to search Dave's desk for the bathroom key.
After locating it, he returned to his studio to hit the head — but opening the door revealed Katie Couric, who, improbably, was in the middle of brushing her teeth. At the end of the bit, Colbert returned the key to Letterman and showed up at the tail end of the "Late Show" monologue.
Why don't more late-night shows do cross-overs like this?