McGlashan spent his youth career with Celtic Boys Club. He signed for Dundee at the start of the 1982-83 season, where he stayed for 18 months and scored one goal in 11 league appearances. McGlashan signed for Dunfermline Athletic midway through the 1983-84 season, where he stayed for 6 months and scored one goal in 16 league appearances.
McGlashan signed for Cowdenbeath at the start of the 1984-85 season, where he stayed for 2 years and scored 27 goals in 60 league appearances. He signed for Clyde at the start of the 1986-87 season, where he stayed for 4 years and scored 48 goals in 140 league appearances.
McGlashan signed for Clyde's fiercest rivals Partick Thistle at the start of the 1990-91 season, where he stayed for 3 years and scored 30 goals in 103 league appearances. While at Thistle, McGlashan was the subject of a famous quote from manager John Lambie; on being informed during a match that McGlashan was concussed and didn't know who he was, Lambie said, "tell him he's Pelé and get him back on".[2]
McGlashan signed for Ayr United at the start of the 1993-94 season, where he stayed for 1 year and scored 3 goals in 36 league appearances. He signed for Montrose at the start of the 1994-95 season, where he stayed for 4 years and scored 67 goals in 141 league appearances. McGlashan signed for Montrose's arch rivals Arbroath at the start of the 1998-99 season, where he stayed for 3 years and scored 33 goals in 88 league appearances.
McGlashan's final professional club was Elgin City, whom he signed for at the start of the 2001-02 season, where he stayed for 3 years and did not score any league goals in the 14 league matches that he played in. McGlashan retired at the end of the 2003-04 season at the age of 40.