WASHINGTON—Investigators have found “serious irregularities” at the federal jail in New York where Jeffrey Epstein was being held on sex-trafficking charges, Attorney General William Barr said Monday, deepening the mystery surrounding the disgraced financier’s death.

Mr. Epstein, 66 years old, was found dead Saturday at the Manhattan detention facility administered by the federal Bureau of Prisons. The New York City medical examiner believes Mr. Epstein’s cause of death is suicide by hanging, but is awaiting additional information...