There was never any explanation given for Dan Briggs' departure.
William Windom who plays the drug dealer Alex Cresnic played 4 different characters in 4 seasons of Mission Impossible.
This was Martin Landau's first appearance in the series as Rollin Hand, credited as a full cast member.
Steven Hill's role was severely reduced for the five remaining shows of season one, and he was not asked to return for season two. Primarily because as an Orthodox Jew, he was unwilling to abide by the production schedule that would have required him to work on the Sabbath; and his disruptive behavior often caused filming delays. Hill was replaced by Peter Graves in the role of Jim Phelps, the new team leader of the IMF.