Other mistake: In the kitchen, when Niles burns his hand you can see him move his hand down to stop the frying pan from falling off the stove. He doesn't touch it again, but it looks like the instinctive actions of someone who knocked something over rather than part of the scene. He just slips out of character for a moment.
Continuity mistake: When Frasier is offering to help Lorna carry her books, her purse switches from her right shoulder to her left arm and back to the right from shot to shot.
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.