On August 16, U.S. District Court Judge Kevin Sharp refused to order a new Democratic Party primary for U.S. Senate in Tennessee. Larry Crim had charged that the primary was flawed and should be re-run. The case is Crim v Tennessee Democratic Party. See this story. The basis for the denial of relief is apparently a technical flaw in the Complaint, which was only filed the day before the hearing.
As noted previously, the person who won the Democratic primary has already been disavowed by the state party, but the state party itself has not taken any legal action to replace its nominee. UPDATE: see this story, which describes the hearing and is unusually funny for an article that describes an election law matter.