Continuity mistake: When Lilith arrives at Frasier's, she is moving her hands, rearranging her wrap and her purse is in her left hand. Without time for her to change it, in the next shot her purse is in her right hand.
Continuity mistake: When Lilith and Frasier are in the hotel room, Frasier's shoes are on the floor by the chair, neatly arranged. When he says "that's very impressive, Dr. Sternin" and walks away, the shoes are not in the same position anymore.
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.