Continuity mistake: Frasier is in Mr. Safford's study talking to him. As Frasier says "a little unconventional," his right hand goes up to his chin, gesturing. As Safford answers, Frasier's hands are grasped together in front of him, with no time for natural change.
Continuity mistake: Frasier is arguing with Niles in the kitchen and removes a large bottle of water from the fridge. He takes off the cap, and pours water into a glass. Immediately the shot shows the bottle capped again while Frasier and Niles continue talking.
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.