(At 00:18:55) Frasier and Niles are standing just out of reach of the white horse behind Martin. Two cuts later, Frasier and Niles are standing in exactly the same stance but closer to the horse with no time for them to have moved given that they are trying to be quiet, and the horse begins licking Niles' face.
When Frasier begins to tear up his binocular receipt he tosses his wallet onto the newspapers in front of him. Once he finishes ripping up the receipt, the wallet is no longer shown.
In a season 1 episode, which aired January 1994, Frasier tells Daphne his father is 63 years old. Yet in this one, which aired in September 1997, they are throwing his dad a 65th birthday party. Doesn't add up.
The huge TV Frasier buys for Martin looks to be at least 10 feet tall. It would be impossible to fit the TV through the apartment door.
When Eddie is jumping in order to try to look over Frasier's newspaper, rather than look at Frasier, he looks straight up, making it obvious that he is trying to reach a treat that's suspended above him. Even after he stops jumping, he looks up one last time.