When Martin invites Frasier and Niles down to Dukes, he introduces them to Duke as if they had never met him before, but in "First do no harm (#6.5)" Frasier and Niles talk about spending time with Duke and his daughter Marie when they were kids.
Frasier refers to a former Pony Express office in Seattle. At no time did Seattle ever have a Pony Express office.
When Niles jumps up to sit on the console, he bump into a control board. It moves. Any studio control board would either be screwed down to make it immobile or counter-sunk to restrict movement. Niles also hits a live microphone button which caused a loud, high-pitched feedback. Every mic on a control board is routed though a relay that turns off in-studio monitors specifically to prevent feedback.
When the wrecking ball crashes through the window of Duke's, the breeze causes a ripple in the facade of the furniture store across the street, revealing that the street scene background is a painted backdrop.
A building set for demolition would most certainly be locked up, yet Martin and Frasier are able to get in without a key. Also, before wielding the wrecker's ball, the demolition crew would first check to make sure no one was inside.
It's well after midnight when Daphne comes home from her date, but the buildings outside Frasier's apartment are lit up as if it were mid-evening.
While Fraiser and Martin discuss why Frasier has not previously been invited to Duke's, Martin states it's because it is the type of place he would look down on. However, Frasier use to hang out at Cheers, which is a similar blue-collar bar like Duke's.