The Citizen Smith change has been mentioned, but this is what really happened: Antro Morris was replaced by Peter Vaughn, Peter Vaughn was replaced by Tony Steedman.
Here is how the 'Last of the Summer Wine' third man scenario went.
1973-1975: Bill Owen, Peter Sallis and Michael Bates
Michael Bates left due to bad health, so he was replaced by Brian Wilde
1976-1985: Bill Owen, Peter Sallis and Brian Wilde
Brian Wilde left and was replaced by Michael Aldridge
1986-1990: Bill Owen, Peter Sallis and Michael Aldridge
Michael Aldridge due to family reasons and he was replaced by the man he replaced, Brian Wilde
1990-1997: Bill Owen, Peter Sallis and Brian Wilde
Brian Wilde left due to a minor ailment, so he was replaced by Frank Thornton
1997-2000: Bill Owen, Peter Sallis and Frank Thornton
Bill Owen died, so Peter Sallis became the first man, Frank Thornton was promoted to second man and third man went to a cast-member already in the cast, Keith Clifford
2001-2006: Peter Sallis, Frank Thornton and Keith Clifford
Keith Clifford left the series in 2006 so like he did, his place was replaced by someone who was already in the cast, Brian Murphy
2007-date: Peter Sallis, Frank Thornton and Brian Murphy.