Continuity mistake: Frasier is at Cafe Nervosa and tears off the edge of a sugar packet which he leaves on the table. Subsequent shots sometimes show the paper there, and sometimes not.
Continuity mistake: When Frasier is talking to Patrick Stewart (who is putting his coat on) in Cafe Nervosa, the collar on Patrick's coat fixes itself between shots, without him doing anything to it. In particular, one of the lapels is stuck under the coat for one shot and is suddenly normal in the next shot.
Continuity mistake: When Frasier prepares to leave the gay bar, he puts his sherry glass on the bar and pulls back - but the next shot shows him pulling back from the bar again.
Continuity mistake: After Gil comes into Frasier's booth to talk following the 'outing' caller, Frasier begins packing his briefcase, then shuts it. Seconds later, it is still open and he shuts it again.
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.