PORT ST. LUCIE, Fla.—During their disappointing 2012 season, the Jets became known for the butt fumble, caused by quarterback Mark Sanchez's unfortunate collision with teammate Brandon Moore's rear end. Across town, the Mets are countering with a derrière distinction of their own: the butt dialer.

That would be Jay Horwitz, the team's longtime director of media relations. Several times per week, and sometimes several times per day, Horwitz accidentally calls a current or former member of the organization. He has mistakenly...