Add “paying her rent” to the list of Mischa Barton‘s problems. The wild-child former “O.C.” star is getting sued by MRA Realties for allegedly stiffing it on three months’ rent for a $7,000-a-month loft on Walker Street. Neighbors said she cleared out of the building late last year, and they aren’t tearing up over the loss. One told The Post’s Edmund DeMarche, “When she wasn’t partying, she was moving furniture. She was always making noise.”