He scored one goal in the 1961–62 Inter-Cities Fairs Cup, in a 5–2 home victory over Lyon; Wednesday went on to reach the quarter-finals, where they were knocked out by Barcelona after a 2–0 defeat at Camp Nou.
The "Owls" again posted sixth-place finishes in 1962–63 and 1963–64, before slipping to eighth position in 1964–65 under new boss Alan Brown.
Dobson finished as the club's top-scorer with 14 goals in 47 games in the 1967–68 campaign, including one in the League Cup semi-final defeat to Arsenal at Highbury.
He was then a top-scorer for a second time as he bagged 11 goals in 43 matches in the 1968–69 season, as new boss Ian Greaves took the "Terriers" to within ten points of promotion.
Dobson built a successful partnership with Frank Worthington and claimed nine goals in his 33 appearances as promotion was achieved with a first-place finish in 1969–70.
He also played four Third Division games at Pat Saward's Brighton & Hove Albion in January 1972 on a loan deal that was expected to be made permanent.
[3] In June 1972, Dobson signed with Bristol Rovers as a player-coach, having been a former teammate of manager Don Megson at Sheffield Wednesday.
[3] In the summer of 1968, he was selected by the Football Association for a Commonwealth tour of the United States, New Zealand, Malaysia and Hong Kong.
He later worked as chief scout at Stoke City and was credited with the discovery of England international goalkeeper Ben Foster.