SOCHI, Russia—Inhospitable hotels were the big headache of the 2014 Sochi Olympics preshow. After the first day of full competition, it looks like empty seats could become the problem child of the Games themselves.

A few events played to virtual sellout crowds and enthusiastic spectators: notably biathlon, the ski-and-shoot Russian favorite, and team figure skating, in which the home squad held a commanding lead.

But...