During his career at Televisa, Zabludovsky covered several important episodes. He was one of the few Mexicans reporting in Cuba the day Fidel Castro entered Havana in 1959 during the overthrow of the Batista dictatorship and reported from his car phone (at that time these car phones were the only mobile phones in Mexico and were a luxury item), and reported on the 1985 earthquake that destroyed several parts of Mexico City. However, there was criticism of his coverage of presidential elections in 1988 and 1994, when he favored the candidate of the government party to the exclusion of opposition contenders.