While Phoebe is talking with her father in the coffee house, she doesn't mention to him about meeting Frank Jr. or her birth mother, Phoebe.
In the uncut DVD version, there is an alternate ending where Phoebe calls Ursula to tell her about their father, and Ursula's part of the conversation is repeated by Phoebe for the audience's benefit because Ursula isn't shown or heard directly. At first Ursula doesn't recognize Phoebe but when she does she says to Phoebe that John Glenn is their father to which Phoebe says that he's not. But Ursula urges Phoebe to file a law suit against him to which Phoebe says she won't. Ursula then says to Phoebe that John Glenn wasn't there when they were growing up to which Phoebe says that it doesn't matter because he is not their father. Ursula says that that is for a jury to decide.
Phoebe is left handed. This was shown in The One with Joey's Bag (1999), during the scene where Phoebe meets her father in Central Perk.
Bob Balaban, who portrayed Phoebe's father Frank Buffay Sr, later guest-starred on an episode of Web Therapy (2011), starring Lisa Kudrow.