Faye says that her mother Helen saw Frasier shopping for a menorah when assuming that he is Jewish, but Frasier was shopping for a sweater for Roz when he met Helen.
Helen is standing behind Roz and Frasier when Frasier explains why he bought for a menorah for his son Freddy, and she overhears their conversation. Helen is visible over Roz's right shoulder during the conversation.
Roz refers to Frasier's son Frederick as being "half Jewish". There is no such thing since according to Jewish law a person is Jewish if born of a Jewish woman (as is Frasier's ex-wife Lilith, Frederick's mother).
When the Christmas tree is being hidden in the entryway restroom and the door gets slammed the upper part of the wall between that door and the front door wobbles like a set piece, not a luxury residence.