Continuity mistake: Frasier is in the hospital waiting room and Phil (the guy who later pretends he is Frasier) is reading a newspaper - he folds it up before talking to Frasier but in the next shot, from another angle, we see him folding it up again.
Continuity mistake: Niles has just met Mel in her office, and she is wearing a white coat - she is brushing off her sleeve in one shot, and then unbuttoning the coat in the next, without enough time to have switched that quickly.
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.