"That is an extraordinary run of events for a city that seven years ago was 15 feet under water and the last on every list in America that mattered," Mayor Mitch Landrieu said last week. "Now we find ourselves in a city that's on the world stage."Yet, as far as the city has come, decades-old problems persist. New Orleans remains plagued by violent crime, political corruption, a troubled police department and poverty. Crime rates briefly dipped after Katrina scattered residents all over the country but quickly soared again as people returned home. Landrieu has made crime reduction one of his top priorities, but the murder rate has remained stubbornly high since he took office in 2010. After the storm, federal authorities launched a sweeping effort to clean up the police department. Several investigations yielded charges against 20 current or former officers, many of whom were linked to deadly shootings in Katrina's chaotic aftermath. The Justice Department also has negotiated ambitious plans to reform the police force and improve conditions at the city's jail. Separate probes of City Hall corruption revealed that some officials enriched themselves while New Orleans struggled to rebound from the storm. The latest and most prominent target so far is former Mayor Ray Nagin, who was indicted earlier this month on charges he accepted bribes and payoffs in exchange for steering work to city contractors. For the city's poorest residents, life hasn't gotten any easier since Katrina. Housing costs have skyrocketed while the region's unemployment rate has risen along with the rest of the country. A months-long moratorium on deepwater drilling in the Gulf after the BP spill didn't help matters, either. "A fresh coat of paint hasn't and won't drive away the poverty that has existed in our community," said Davida Finger, a Loyola University law professor who has helped low-income residents with Katrina-related housing problems. "It didn't go away with the storm, and it can't go away overnight."