Danny's party is filmed outside Monica and Rachel's apartment. If you look through the crack in the door behind Monica you can see the colors of her apartment.
The message on the Magnadoodle reads: "No girls allowed!"
The music playing at Danny's party is "Every Word Means No" by Smash Mouth. This track is also played on Dick Clark's New Year's Rockin' Eve in The One With The Routine.
When Rachel and Monica are in the coffee house Rachel makes a comment that she "doesn't go after guys right after they get divorced". Earlier in the series she went after Joshua who had just gotten divorced - most likely she doesn't go after recently divorced men because of Joshua.
Ross' outgoing message is to the tune of Queen's "We Will Rock You".