In 2005 he sent off 21 players in 16 league games. During a 2005 match that faced San Felipe against Unión Española, the latter's goalkeeper Ignacio González received his second yellow card, and consequently a red card. Upset by this, González brought Osses to the ground after hitting him in the face. Afterwards the player was held in police custody for two hours. He faced a ban of up to 50 matches, which he did not serve because he left the team, to play in Argentina.
In March 2013, FIFA named Osses to its list of 52 candidate referees for the 2014 FIFA World Cup in Brazil. Several of his calls during the Costa Rica v. Italy match was hotly disputed in various social media.