Having just completed reading The Guns of August, Barbara Tuchman's book about the first month of WW1, I think there are a few obvious PoDs. The most obvious one is for the BEF to not take part. OTL, Sir John French as well as Murray, his chief of staff had both refused to join Joffre's battle plan. It was only thanks to a last minute personal visit and emotional plea from Joffre that Sir John was convinced to fight. Without the BEF holding a crucial part of the line between the French Vth and Paris Armies, there would have been a giant hole throw which the Germans could have easily gotten through and outflanked the French.
Another obvious one is for von Moltke to stick rigidly to the Schlieffen Plan and to obey his dying words i.e. ' Only make the right wing strong'. To do this, Prince Ruprecht's Southern counter-offensive would have to be cut short and his men would have to be sent to reinforce the German right wing after the Battle of the Frontiers. This would also mean no last minute transfer of resources to the Eastern front to face down the Russian armies that would have been deal with at Tannenberg. No weakened right flank might mean a German Army with enough of a numerical advantage to resist the Allied counter offensive and keep marching on.
But my favorite PoD, although it relates to an earlier battle, is for General Lanrezac, who was commanding the French Vth army that was sent into Belgium, to stick to his hyper-offensive theories and not withdraw during the Battle of Charleroi. This would have ended in a Sedan-like encirclement and surrender for the outnumbered French. With no support on either flank, the BEF would probably have made a bee-line for the Channel while the rest of the French Army would have been completely surrounded as Schlieffen originally intended.