The description on the site for this quest is wrong. The mime now needs to be taken to the NE corner of Pseudopolis yard. The room description reads:
Although this northeastern part of Pseudopolis Yard offers the uglier side of the Ankh-Morpork Opera House for inspection, the monstrosity sits comfortably, quietly confident in its domination of all surroundings. The Publishing House to the east is quiet now, though a small light above the otherwise indistinguished door set into the wall to the north seems to suggest that whatever goes on in there continues well into the night.