When Daphne yells at Eddie for drinking water from the toilet and Frasier comes out apologizing and they both scream you can see that Eddie is not at the toilet anymore but it would be unlikely that he just ran off that quickly.
In this episode we learn that Daphne has to take a "prescription" pill before bedtime. In Season Four's "Daphne Hates Sherry", we learn that they are for a thyroid condition.
Although Frasier promises, Daphne's room never does get redecorated (apparently the car was enough). We can see this in Season Three's "Come Lie With Me", wherein Daphne's room still has the same Burnt Sienna walls and blonde furniture and woodwork. The only change is that the bed has been moved in front of the window.
Daphne closes both her closet and room doors before entering the shower. Yet, when Frasier is discovered and runs out moments later, the door to the hall is completely open.
This episode contains the first bit of trivia that Maris comes from a Roman Catholic background. Niles mentions that she nixed the idea of a French-themed party by reminding him that a branch of her family were slaughtered by the Huguenots; French Protestants, who engaged in armed conflict with the majority Roman Catholics in the 150 years after the Protestant Reformation began.
Frasier: If you're through marinating in your own testosterone, I have a problem. Remember last night I went back into Daphne's room? Well, she caught me again.
Niles: You're joking!
Frasier: I was just so embarrassed I had to leave this morning before she woke up. I left a little note, trying to explain my actions. Considering the circumstances, I don't think there's any way she can forgive me!
Niles: Oh, come now. It wasn't as bad as all that. It's not like you saw her naked or something.
(Frasier looks at his feet, Niles can't believe it)
Niles: You did!
Frasier: But I took no pleasure in it at all! The entire thing was just absolutely mortifying!
Niles: Frasier, I want to help you with this, so you have to tell me everything. Every sight, every sound – Frasier, unburden yourself before you explode! (he says about to explode himself)
Frasier: No, Niles, no!
(Niles takes out a pen and grabs a napkin)
Niles: Alright then, I'll show you how I've always imagined her and you tell me where I'm wrong!
Niles mentions that a branch of Maris's family were massacred by the Huguenots, who were French Protestants who were often at war with the Catholic majority in that country in the years following the Protestant Reformation.
The title to the first act is "Where no man has gone before" which is clearly an allusion to Star Trek, the original series. The words are spoken by William Shatner (Captain Kirk) during the show titles and the words are also the title of the second pilot episode.