Hillary Rodham Clinton brings a quarter-century of public service to her potential presidential campaign, but it’s her most recent job as secretary of state for President Obama — overseeing relations with Russia, handling the terrorist attack in Benghazi and negotiating over the war on terrorism — that could come back to haunt her. Many of Mr. Obama’s current political problems also could affect Mrs. Clinton, including the handling of Russian President Vladimir Putin and the decision not to slap the terrorist label on Boko Haram, a group responsible for kidnapping hundreds of Nigerian schoolgirls last month. Even the Keystone XL...