For his "ballhawking" skills, Dillon was nicknamed "The Hawk" by his Packer teammates. In his career, Dillon recorded 976 interception return yards, including five he returned for touchdowns. Dillon's 976 interception return yards is the most in Packers' history, and in 1956 he had a league-best 244 interception return yards. Dillon also shares the team record for interceptions in a game, with 4, which he recorded in a loss against the eventual NFL-champion Detroit Lions in the 1953 Thanksgiving game. With less than two minutes left in his record-setting game, Dillon injured his knee, which caused him to the final two games of the 1953 season. Despite missing those two games, Dillon finished 1953 with nine interceptions and was healthy enough to return at the start of 1954.