Factual error: When Josh Hartnett's character pulls up the bathroom tile and find the cash, the bills are labeled "Federal Reserve Notes." Federal Reserve Notes didn't come into use until the 1960s. Back at the time of the Black Dahlia murder, Silver Certificates were in use.
Factual error: The Black Dahlia is shown smoking a "cork tip" filter cigarette. In the 1940s, cigarettes had no filters and the paper on the "stick" was all white.