After his gun goes off, damaging a tile above the fireplace, Martin tells Niles to get him some spackle. After running around aimlessly for a moment, Niles finally asks Martin, "What's spackle?".
Niles should know. In Season 10's "The Harassed", he complains that the remodeling of his office has caused his spackle allergy to act up.
It seems highly unlikely that a veteran cop like Martin would keep a loaded gun in the house, even in a hidden place. Keeping ammunition separate from the weapon in the home is one of the very first rules of gun safety.
Daphne tosses Niles a banana which he fumbles, knocking a shoe box to the floor which contains his father's gun. You can see David Hyde Pierce desperately trying to grab the banana as he needs it for his next line, but when the gun fires, he jumps back, losing the banana in the process. In the very next scene, however, Niles is holding the banana as he says, "I think the banana went off!"
In all episodes following this one, the replaced tile over the fireplace (broken by the bullet accidentally fired from Martin's gun) can be seen to be a shade darker than all the others.
In the hotel room scene after Lilith and Frasier spent the night together on the couch, the carpet can be seen coming to an end when the camera zooms out; this proceeds to reveal hard, black flooring in front of the set.
When Niles stands up you can see that he is not actually completely undressed because you can see a bit of his tan undies.
Frasier suggests that he and Daphne go to his place since the phone is going to ring all night at Niles's.
Why don't they simply disconnect it?
The televised news clip of Frasier stating that "Maris Crane and Niles Crane will soon be executed" is spoken with significantly different inflection than the statement that Frasier is shown delivering in the previous scene.
Frasier says that Niles had a breakdown in his senior year because his girlfriend left him for his roommate. However, Niles has indicated that there was so few women before Maris, so few women after Maris, hence there was Maris. The only women were his pen pal Dora from Costa Rica and the little girl who showed him her underpants.
Daphne was furious with Maris because of the trouble she caused the two of them. Maris caused a lot of trouble for Niles but barely touched Daphne. And Daphne met Donny because of that little bit. Mel on the other hand...
In the opening scene of this episode, the piano is just above the living room area instead of just above the dining room area where it has been since the show premiered. While the piano is clearly on wheels, it seems unlikely that they'd move it out to play.
Martin should know that Roz is Frasier's producer, not his "secretary."
The book that Ann carries with her is Likely To Die by Linda Fairstein.
When Frasier pays the check and is trying to get rid of Ann and she says "there's no sense in all this food going to waste" and takes out her book Frasier sees that she is not going to leave right away he could have suggested like he did before for them to wrap her food up so she could leave right away.
Twice at dinner with Ann, Frasier says that his phone has rung when no one else can hear it. When questioned, he need only have said that it was set on vibrate -- a considerate setting in public places where others might be disturbed.
Frasier was allergic to cats in "It's Hard to Say Goodbye If You Won't Leave", yet here he has no problems with them.
Martin: (to Frasier about Ronee) I thought you brought her here for me.
Frasier: Since when do I bring you women? What are you, the Sultan of Brunei?
The current Sultan of Brunei, one of the wealthiest men in the world, has two wives. His former second wife was an airline stewardess, and his current second wife, was a TV personality, 33 years his junior.
If you look closely at the top right hand corner of the room screen in the left of the opening shot you can see a lump of chewing gum. Moments before filming began Kelsey Grammer realised he was still chewing and didn't have time to put it anywhere else.
For the studio audience Kelsey Grammer and Peri Gilpin did a read through of the scene at KACL that would later open the episode Freudian Sleep - where Frasier doesn't have any callers and makes Roz phone into the show - because they were going to include the scene in this episode but weren't going to film it that night.
After calling Martin the "Sultan of Brunei," Frasier grabs his wine glass with one hand on the top and walks out of the kitchen. In the next shot when he is coming out he is holding it by the neck and there was no time for him to change his grip.