Had Hearst been nominated by the Democrats in 1912, he would have likely become POTUS given the Republican/Progressive split that year.
This could have a big impact on foreign policy! Hearst was an isolationist concerning Europe, and he hated the British Empire -- BUT concerning Mexico (just like Cuba 15 years earlier) he was a big advocate for U.S. intervention and war during the Mexican Revolution.
According to The Chief: The Life of William Randolph Hearst by David Nasaw, Hearst wrote in a November 1913 editorial "There is only one course to pursue. That is to occupy Mexico and restore it to a state of civilization by means of American MEN and American METHODS."
Wilson did send troops to Mexico for several fairly limited interventions, but it wasn't enough for Hearst, who accused him of capitulating to Mexico by agreeing to international arbitration.
Things got more heated in December of 1915, when the forces of Pancho Villa seized Hearst's million-acre Mexican ranch and confiscated his cattle and sheep for food, and horses for transport. It became a personal vendetta for him. And Hearst wasn't prone to putting aside personal vendettas.
Ben Procter's William Randolph Hearst: The Later Years :
'Hearst continued to be extremely unhappy with Wilsonian efforts in Mexico. In a barrage of editorials he railed against the administration. [. . .] "Our army should go forward into Mexico, first, to rescue Americans, and, secondly, to redeem Mexicans" (May 3, 1916) [. . .] Intervention in Mexico is not for the purpose of MAKING war. It is for the purpose of ENDING war [ . . .] since the policy of neglect of duty has so utterly failed to secure peace and justice, let us try the policy of active performance of duty. (July 9, 1916)."'
Around this time, Hearst was also investigated by the FBI (or, back then, just the BI) for "secretly financing Mexico revolt near his ranch in Mexico [and] helping to fit out a Military Expedition in this country directed against Mexico." (William Randolph Hearst: Media Myth and Mystique by Daniel Alef).
So we've got President Hearst strongly advocating for war in Mexico years before the Zimmermann Telegram. Under certain circumstances, this could lead to WW1 expanding to the Americas in some form or another! A really underrated POD.