This is explained in the episode of Frasier when Sam Malone comes to visit. Malone reveals to the senior Crane that Frasier said he was dead. Martin asks Frasier why he would do such a thing and Frasier response:"We had just had a fight!"
If you watch the episode of Cheers where this slip-up is made, Frasier is telling one of the gang how his father died before he could he tell him he loved him and was proud of him or something like that. It was very sentimental, not at all like anger over a fight.
This isn't really a slip-up but on one episode of Cheers Rebecca hires someone to write and perform a jingle for cheers, the man she hired was John Mahoney (Frasier's Dad on Frasier).
Eric, he could have been faking his sorrow to hide his anger.
The actual dialogue was more like this: Sam wonders how Frasier's dade Martin could be alive when he told him he was a scientist who died. Frasier tells Sam that he was made at his dad and made that up. To which Martin says:
"But why did you say I was a scientist?"
(On Frasier he's a retired police officer.)
Frasier: What did it matter? You were dead!
Along those lines....in an early episode of Cheers, Fraser introduces Diane to his b**chy mother who threatens to kill her. But Frasier's mother is supposed to be poised, intelligent and dead...???
The one about Frazier's dad is not really a slip up. In the CHEERS series, Frazier says that his father has passed away. In the FRAZIER series, when Sam meets Frazier's dad, Sam asks Frazier why he had told them he was dead. Frazier replied that he was going through an argument with his dad at the time. So technically, it is not a slip up !