McCourt played major junior in the Ontario Hockey Association (OHA, renamed OMJHL during his tenure, today's OHL). As a 15 year old, he was already playing Tier II junior hockey when called up by the Sudbury Wolves for part of the 1972–73 OHA season. He joined the Hamilton Red Wings for the full 1973–74 OHA season, and was team captain by the time the (renamed) Hamilton Fincups won the 1975–76 OMJHL Championship and then the national 1976 Memorial Cup championship.
In 1976–77, McCourt led the relocated St. Catherines Fincups as the team won the OMJHL Regular Season Championship. That season, McCourt was awarded the Red Tilson Trophy as the league's Most Outstanding Player, and was voted the nationwide CHL Player of the Year. Dale was also awarded the William Hanley Trophy as the OMJHL's Most Sportsmanlike Player in both 1975–76 and 1976–77.
In the 1977 World Junior Ice Hockey Championships, McCourt scored 18 points, a Canadian record he shares with Brayden Schenn and one point more than Eric Lindros and Wayne Gretzky.
McCourt was drafted 1st overall by the Detroit Red Wings in the 1977 NHL Amateur Draft.
McCourt led the Red Wings in scoring during his 1977–78 rookie season, finishing second only to Calder Memorial Trophy winner Mike Bossy for rookie scoring in the NHL that year.
Before the start of the 1978–79 season, Red Wings general manager Ted Lindsay signed Rogatien Vachon of the Los Angeles Kings, who was a restricted free agent at that time. An NHL arbitrator ruled that McCourt should be the compensation paid the Kings for Vachon's loss, but McCourt refused to report to the Kings. Ultimately, this led to McCourt suing the NHL, National Hockey League Players' Association (NHLPA), the Red Wings and Kings in order to prohibit being sent to the Los Angeles Kings as a part of any compensation package. During this lawsuit, McCourt remained playing for the Red Wings, finishing the season second in Red Wing scoring (behind by only two points) for 1978-79. The matter was resolved and McCourt remained in Detroit, but he felt betrayed by the fact that his own NHLPA, led by Executive Director Alan Eagleson (convicted in 1998 after years of embezzling from the NHLPA members), did not back him against the owners during the lawsuit.
McCourt continued to be the Red Wings top scorer in both his third (1979–80) and fourth (1980–81) seasons. Despite this, and while leading the team in scoring a third of the way through the 1981–82 season, management did not feel he had achieved their overall expectations, trading McCourt to the Buffalo Sabres in December 1981—having produced at a point-a-game pace during his time with the Red Wings but failing to make the playoffs for three of his four years with the team. He played with Buffalo until being traded to the Toronto Maple Leafs in October 1983, finishing his NHL career at the end of that 1983–84 NHL season, with 478 points in 532 games played.
McCourt then played for 6 seasons for HC Ambrì-Piotta, in the top Swiss league. Ambrì-Piotta retired McCourt's number 15 jersey.
McCourt's brother Dan was an NHL linesman during the 1980s and early 1990s.
McCourt's uncle is Hockey Hall of Fame member George Armstrong. Armstrong won the Red Tilson Trophy as the OHA's Most Outstanding Player in both 1947–48 and 1949–50, the same award that McCourt received in 1976–77. Armstrong was the coach of the Toronto Marlboros when they won the national Memorial Cup Championship in 1973 and 1975, the same championship that McCourt won as a player with the Hamilton Fincups in 1976.Directorate Award, Best Forward, 1977 World Junior Ice Hockey Championships