Frasier tells Woody what he and Lilith did during their first romantic interlude, but Woody and the rest of the Cheers gang would know that what happened, as shown in "Abnormal Psychology (#5.4)" (1986), was completely different.
In the second half of the show when the Cheers regulars are discussing their rivalry with Gary's Old Town Tavern, the dart players in the background are miming playing darts, and not actually using darts.
While Frasier does say BOTH of his parents are dead, in the 2nd season Fraiser episode "The Show where Sam shows up", Sam mentions this and Frasier tells his stunned father that they were having a fight and not talking at that time.
Frasier says that St. Patrick's Day is the day Saint Patrick drove the snakes out of Ireland. According to tradition, the patron saint died on March 17 and the holiday is actually an observance of the his death.
Frasier states that he can't ask his parents to babysit because they're dead, however, his mother, played by Nancy Marchand, was seen in a previous episode and no mention was ever made of her death, whereas Frasier's father, Martin, is obviously alive in the spin-off series.
Fraisier is looking for a babysitter so he can have a romantic evening with Lilith. When Sam suggests asking his parents, Fraisier says they are both dead.