So much for buying them off with buttons and discounts: At a moment when city officials and the protest's organizers, United for Peace and Justice, should be polishing the final details over the event next Sunday, they are instead locked in a court battle over the route of the march, which organizers say could draw 250,000 people. The group itself is fractured over how to proceed, and many protesters are vowing to use Central Park despite the vehement opposition of the city, which wants the rally to take place on the West Side Highway. Adding to the uncertainty are the boiling tensions between Mayor Michael R. Bloomberg and officials and members of the police and firefighter unions, many of whom have been trailing him at his public events for weeks demanding a new contract and threatening illegal strikes or other job actions just as the city struggles to deal with the protests and the convention...the potential for embarrassing or explosive confrontations between protesters and the administration is increasing as the start of the convention looms closer without final arrangements being set. Some officials and protest organizers fear a repeat of the rally against the Iraq war in February 2003, when demonstrators and the police clashed, leading to hundreds of arrests, in large part because plans for the event were not completed until the last minute. The situation has created a headache for Mr. Bloomberg, who is counting on a convention that will be good for the city's image and show the world how it has recovered from the Sept. 11 attack. Further, Mr. Bloomberg has to find a careful political balance between the tough labor stance he has taken with the uniformed officers and his desire to not inflame this group of city workers, who were lauded for their role after the terror attack.