Where There's Smoke There's Fired - S3-E21
Continuity mistake: When everyone is sitting at the table having dinner, the amount of food on Bebe's plate changes repeatedly. She adds extra food twice, once from the pot and once from Martin's plate, but the difference in portion sizes changes more times than that and without time for it to be eaten. (00:11:05)
Where There's Smoke There's Fired - S3-E21
Continuity mistake: Bebe has just inhaled smoke from her purse and Frasier grabs it and puts it on his bookcase. In the shot before, there had been billows of smoke around them, but suddenly the air is clear and there is no smoke.
Where There's Smoke There's Fired - S3-E21
Continuity mistake: When Frasier, Bebe, and the rest of the gang are having dinner at Frasier's he folds up his table napkin and says "he's on his third pacemaker", and we see him fold up his napkin 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.