Dwyer remained a mainstay of the side for more than a decade, becoming known by the nickname "Joe" due to his perceived resemblance to Joe Royle. He was nearly released by manager Len Ashurst in 1982 following a serious knee injury. He returned to the first team, winning promotion in the 1982–83 season and was ever present during the 1983–84 campaign. He set a new club record for Football League appearances the following year, overtaking Tom Farquharson's long standing record. Dwyer left the club in 1985 after falling out with manager Alan Durban. He made 575 appearances in all competitions for the club, scoring 51 times during a 13-year spell. He made his international debut for Wales in April 1978 and gained ten caps over the following year, scoring twice. He won his last cap in October 1979.