It varies from performance to performance. "Peter" basically talks to the audience throughout the show, narrating events of his life. If people come in late, he will focus on them, asking why they were late and let them know what they missed.
In the second act, he opens with the song Bi-Coastal and after it's over he picks someone from the audience and interacts with them. What exactly he does depends on the person picked. I heard that Elvis Costello was in the audience recently, and "Peter" got him up on the stage to jam with the band.
When I saw the show twice in June, Peter's choice of participant was a teacher from Melbourne who was seeing the show with his students. The teacher, Steve, was getting an upgraded seat courtesy of Peter -- from rear mezzanine to the orchestra -- but he had to "pay" for the privilege by doing a dance -- and the students got to choose. They chose a lap dance

. Steve did a fine job, matching Peter move for move, even going so far as to take off his shirt. Steve was a big hit.
The second time, Peter's participants after Bi-Coastal were four men from Chicago who were sitting in the front row. They were made to get up and dance in their seats, first facing Peter, then facing the audience. Then, because one of the backup singers was new, Peter put the spotlight on her, and had the "boys from Chicago" come up to the stage and be her dance group as she sang New York, New York.
It was all great fun.