In this episode, We see Martin's brother, Walter, but in a previous one , after Niles and Frasier had a fight and weren't talking to each other, Martin started telling a story about he and his partner on the force, in his opening sentence, he says " I never had a brother, but i had a partner once....".
Which is in contradiction with what we see in "Beware of Greeks".
In the aforementioned episode, Martin admits to Daphne that the story about his partner was made up, so he may have also been lying about not having a brother.
When talking to Daphne (at the table when they are secretly being taped), Martin opens and unfurls his napkin twice
We see Niles looking out the window in the kitchen door. Frasier goes in to talk with him. At which point he says Yvonne is in the men's room. Even though she is standing just outside and to the left of kitchen doors.
During the wedding scene when Martin asks Eddie where the camera is, the boom mic shadow is visible, lowering behind Eddie over the kitchen.