Plot hole: While the wedding party is getting ready to leave Charlotte's apartment, Big calls Carrie's cell phone. Lily (Charlotte's young daughter) answers, immediately closes it without speaking, then drops the phone into her purse that she takes with her to the wedding. Big continually calls back, but even though Lily is always with one of her parents, no can hear Carrie's phone is ringing inside Lily's purse. Lily only closed the phone, it was not turned off, the ringer was turned up, and the battery was charged. Lily and Harry rode to the library separately and during the time Big had been trying to call Carrie. Harry should have heard the phone.
Plot hole: In the scene where Louise gives Carrie her new phone, she tells Carrie of her new phone number and Carrie gets upset because she has lost her old 917 prefix; but all Carrie did was throw her phone away into the ocean, she didn't have to change her number. I'm sure, as here, in New York people lose or break their phones constantly. It's just a chance to explain why Big hasn't got her number - her new number - so he couldn't call her and apologise (but what about her home phone number; that wouldn't have changed - Big would know that number, surely).