While 2013 will be a tough year for retailers due to the tepid economic recovery, a few in particular face a critical 12 months. Their experiences highlight the challenges facing store chains, from increasingly cautious consumers to fierce online competition. These unlucky retailers are going into the New Year with extra woes: slipping sales, questionable strategies and tight finances—which is why they are the ones to watch, and not in a good way. Best Buy Co. BBY -1.22% has been plagued by the retail phenomenon called "showrooming," where shoppers examine products in its stores but buy online through rivals. A...