Matt LeBlanc had a fever and flu the first day. He was at 102 degrees during the pilot and had to repeatedly use a variety of remedies to attempt to cure it.
NBC executives were worried that the content of the show was too racy and that the audience would dislike Monica for sleeping with Paul the Wine Guy on their first date. After the taping of the pilot, the studio audience was given a questionnaire regarding Monica's promiscuity by NBC, and the survey results indicated NBC was worried for nothing, as the audience didn't care.
When Monica goes to get Ross his coffee, a very brief shot of Rachel can be seen passing the doors to the coffeehouse, presumably on the way to Monica's apartment. However, one must look very carefully to see this.
Joey and Chandler pour their Rachel-made coffee into the plant on the table. At the end of the episode, the plant on the table is dead, likely as a result of Joey and Chandler pouring coffee in it.
The interstitial music and city scene after Rachel is shown sitting at the bay window to her preparing coffee for Joey and Chandler originally featured a shot of the Brooklyn Bridge with the World Trade Center towers prominently in the background. After the September 11 attacks, the interstitial scene was changed to a shot of the exterior of the building where Monica, Joey, and Chandler live. However the original scene can be seen on DVD releases published prior to the attacks.