It's Hard to Say Goodbye If You Won't Leave - S3-E10
Continuity mistake: When Frasier and Kate are in the airport, sitting down and talking, her arms switch back and forth from being folded to unfolded (holding her boarding pass). This happens a couple of times, without time for her to change position.
Answer: It equals the record of James Arness of "Gunsmoke" for the actor who's played the same part on TV NOT in a soap opera. If you include soaps there are two main contenders - William Roache, who's been playing Ken Barlow in "Coronation Street" in the UK since 1960. Don Hastings has been playing Robert Hughes in US soap "As the World Turns" since 1960 as well.