Dickenson is considered by many to be the greatest quarterback ever to play for the University of Montana. He owns numerous Big Sky Conference and Montana records. By the time he graduated in 1995, Dickenson had the highest completion percentage, highest percentage of passes for a touchdown, and fewest interceptions per pass in NCAA Division I-AA history. In his college career (including playoff games) he completed 1,015 of 1,477 passes (68.7%) for 13,486 yards (12,332 m), with 116 touchdowns and only 26 interceptions, and was responsible for 137 total touchdowns (116 passing and 21 rushing).
In 1995, Dickenson's senior season, he threw for 5,676 yards (5,190 m) in fifteen games, including 1,500 in four playoff games. After leading the Grizzlies to the I-AA national championship in 1995, Dickenson won the 1995 Walter Payton Award as the outstanding offensive player in Division I-AA.
In Montana, he is known as "Super Dave" and "The Legend of the Fall." His college jersey number, #15, was retired by the University of Montana. He is one of only two players so honored. In 1999, Dickenson was listed as the 12th best Athlete to ever come out of Montana in Sports Illustrated's 50th Anniversary Issue. In 2004, he was voted the most popular athlete from Montana in a Sports Illustrated poll.
After generating interest from the NFL following his outstanding 2000 CFL season, Dickenson spent two seasons (2001-2002) in the National Football League. He spent the entire 2001 season as the third string QB for the San Diego Chargers, but was released by San Diego at the end of training camp in 2002 after a disappointing preseason in which he did not get to play in a game. He was then signed by the Seattle Seahawks and served as the third QB for two games before being released on September 24. In October, he signed with the Miami Dolphins following an injury to Jay Fiedler, and served as their third QB until December 3. He finished the season as the third QB for the Detroit Lions for their final two games after Joey Harrington was diagnosed with an irregular heartbeat.
Dickenson signed as a free agent with the BC Lions in 2003. During the 2003 season, in which he led the Lions into the playoffs with an 11-7, 4th place finish in the CFL West Division, Dickenson's 36 touchdown passes and 5,496 yards (5,026 m) were the second-highest single season marks in Lions' history behind Doug Flutie. Dickenson was named Offensive Player of the Month for August 2003, was the CFL Player of the Week in Week 5, and was awarded the Jeff Nicklin Memorial Trophy as the CFL West Division's Most Outstanding Player.
In 2004, Dickenson began the season as the Lions' starting quarterback, but gave way to backup Casey Printers after suffering a knee injury. Printers put on a dominating performance for the rest of the season, but in the West Division Final against the Saskatchewan Roughriders, was forced to leave the game with a shoulder injury in the fourth quarter, with the score tied 14-14. Dickenson, having recovered from knee surgery and shared quarterbacking duties with Printers late in the season, played the rest of the game and threw a touchdown pass in the Lions' 27-24 overtime victory. Dickenson would start and play the entire Grey Cup game against the Toronto Argonauts, which the Lions lost by a score of 27-19.
Dickenson began the 2005 season embroiled in a quarterback controversy with Printers, who was named the 2004 CFL Most Outstanding Player. Dickenson emerged as the starter, and was instrumental in leading the Lions to an 11-0 start (where he played in 9 of the 11 games), en route to a 12-6 season finish. Dickenson set an all-time CFL record with a passing efficiency mark of 118.8. He fell just short of the attempts required to set a further mark with a 74.0% completion rate, due to 4 games missed because of a concussion. Dickenson was named CFL Player of the Month for both July and September, and was Player of the Week twice.
In 2006, he threw for 3,032 yards (2,772 m) and 22 touchdowns while only playing 13 games. He led the Lions to the franchise's 5th Grey Cup title on November 19, 2006 with a 25-14 win over the Montreal Alouettes. Dickenson was named the Grey Cup Most Valuable Player. Dickenson's 2007 season was interrupted early by a serious concussion received on a hit from Saskatchewan's Fred Perry. Jarious Jackson eventually led the team to another first place finish and franchise record 14 wins, but the Lions were defeated in the playoffs with a recovered Dickenson being called on to relieve Jackson. Dickenson was released from the BC Lions on November 26, 2007, after five seasons with the team.
On January 31, 2008, Dickenson signed as a free agent with the Calgary Stampeders, the team where he began his professional career, lives with his family, and where his brother Craig is the special-teams co-ordinator. But this return was short lived, as post concussion symptoms returned, thus ending his long storied career in professional football.
Dickenson retired from football on February 4, 2009.
On May 1, 2009, Dickenson made the transition from player to coach, joining the Calgary Stampeders as an offensive assistant coach. He will mainly be responsible for coaching the running backs but will be involved in other areas of the offence. On December 9, 2010, he was promoted from quarterbacks coach to offensive coordinator.
On December 3, 2014 Calgary Stampeders general manager and head coach John Hufnagel announced that he would hand over the head coaching to Dickenson for the 2016 season.