When Phoebe and Monica are in the apartment and Monica is putting a ribbon around a vase, she ties it and stops to listen to Phoebe but in the next shot she is tying it again.
Major companies do not allow strangers to wander around employee only areas. Therefore, the quartet and Ross would not have been allowed in Rachel's work area.
Joey sings "You've got to pick a Pocket or Two", which is from "Oliver", a different Charles Dickens story. When auditioning for a musical it is common practice to chose a song from a similar show, not necessarily one from the same show.
Ross would not know Rachel's direct phone number (when the phone rings she gets excited by telling Mark its her first call). However, Ross would have been able to call her any number of ways. First, he would have known she was working in purchasing, as the first thing she told him after meeting Mark was that he "worked for a buyer at Bloomingdale's" and the easiest description of the job she talked about non-stop was as executive assistant to buyer in the purchasing department. Even if her name was not yet in the company directory, she would have inherited the same phone extension of the person she replaced, meaning the number was in the directory. All Ross would have to do is tell the receptionist to connect him to the new assistant of Joanna the buyer, who works with Mark, as she reminds him during the phone call, "I told you, we're Joanna's two assistants". Additionally, the very helpful Mark could have given her the extension in advance to give to her family and friends in case of an emergency, as this was in the days before the Friends were using cell phones, and it was common to give your loved ones phone numbers of places you were going to be so that they could reach you. Finally, if all these methods failed, the receptionist could have placed Ross on hold, called someone in HR, and got her extension.
Ross tells Rachel that he had been with Carol for eight years. However, in The One with the Flashback (1996), he said that he was with Carol for seven years. Both numbers are wrong since Ross and Carol had known each other for just six years by 1993 (they met in college, which Ross started in 1987), the year The One with the Flashback (1996) is set. Even if we ignore that episode and go with the version presented in The One Where Monica Gets a Roommate (1994), set in 1994 and according to which Carol had just moved out, Ross and Carol had known each other for just seven years by then.