Roy mentions his parents as if they are both still alive. In later episodes, his mother has been a widow for over a decade.
Lowell says his wife, Bunny, is incapable of talking to strangers. This conflicts with the the later installments "I Ain't Got No Bunny" and "Bye_bye, Bunny" in which she is quite promiscuous.
When Brian is watching television, he turns it on and off and adjusts the volume with a remote control. However, in the closeup on the set, it is an old style set with UHF and VHF turn dials that definitely would not have had a remote control.
When Fay accidentally hits Joe with the frozen leg of lamb, it's clearly a fake and padded prop.