When Rachel is boarding the plane, she hands the flight attendant her passport, which shows a photo of Monica instead of Rachel.
When Chandler and Monica are holding the twins for the first time in the hospital, Chandler has pink and blue hospital bracelets on his left wrist. In the next shot, they are gone.
While Monica and Chandler are holding their twins for the first time, the hospital ID bracelets on Chandler's wrist appear and disappear between shots.
Rachel tells the gate agent at the airport that she is in Seat 32C. However, when she is shown seated on the plane, she's in the fourth seat from the left. Airplane seats are numbered left to right, the leftmost seat being A, the seat to the right of it B, and so on. Given that naming convention, Rachel was sitting in seat D, not C.
In the final scene, everyone puts their keys on the table, and then walk down the hall. There is a final shot of Monica's apartment, and the keys have changed their positions.
At Newark airport, the aircraft Rachel is boarding can be seen, and the gate is connected to the right-hand side of the aircraft. However, the passenger doors on passenger aircraft are normally on the left hand-side.
Phoebe is driving her taxi with the gearshift in the park position.
Phoebe drives Ross from Monica's apartment building in the West Village to Kennedy Airport. For some reason, however, she takes the Triboro (now named RFK) Bridge to leave Manhattan--there are three other bridges between the apartment and the airport that are much closer.
When Ross is at JFK Airport and learns that he is at the wrong airport, on the departure board, there is both a flight to Dallas and a flight to Ft Worth. Passengers flying to the Dallas/Ft Worth area would only be able to arrive at the shared DFW Airport, not each city's individual (smaller) airports.
During the episode, Joey realizes the duck and chick are stuck inside the foosball table. However, foosball tables have no interior spaces in which the animals can get stuck, other than maybe a ball-return slot, but the table on the show has a center-sloped return slot easily big enough for either Chandler or Joey to reach the back.
Monica and Chandler bring home the twins on the day they're born. Even though newborn babies would stay in the hospital for a few days, the filmmakers had the babies brought home early to simplify the story.
In Jewish traditions, a child is not named after a family member unless that person is dead. Monica is Jewish but names her boy child Jack, after her father, who is still alive. Even though her father is still alive, Chandler has input on what the name should be and since his not very close with his father, Monica's father would be the obvious choice.
Rachel is supposed to be on an international flight, but when Ross and Phoebe are standing in front of the departures board, only domestic flights are listed.
In the last scene, two minutes before the end, it is obvious that the babies are dolls.
Joey sits on his handmade sign for a second time, jumps up, and no letters on the word "baby" are smudged. He had just finished painting it a few minutes beforehand - the red paint would still be wet.
When Rachel attempts to board the plane the first time, the man at the desk looks at her passport upside down. Also, the passport picture is of a woman with dark, wavy hair, as though Rachel might have Monica's passport.
At one point, Joey tells Monica to pick his egg roll up off the floor and put it on a plate. It is obvious that Courteney Cox is picking up nothing and putting it on nothing.
Just before Erica gives birth to the first baby we hear the sounds of Erica screaming, but we can clearly see that she is just breathing heavily in and out.
When Rachel finds her boarding pass and runs up to the gate agent (and says, "you are a different person!"), she cuts in front of a couple; this couple is the same set of extras as who were sitting behind the orange couch during the coffee house scene, earlier in the episode, when Gunther proclaims his love to Rachel.
When Ross and Phoebe go to see Rachel at JFK airport, they make a big point of having to stop and buy tickets so they have boarding passes to get through security. However, when they go to Newark airport they make it all the way to the gate but are blocked from seeing Rachel because they don't have boarding passes. Post-911, all airports require boarding passes to get through security, but it is never explained how Ross and Phoebe slip past security in Newark without them.
Ross & Phoebe still go to Newark Airport although Rachel said on the phone that she has already boarded. They couldn't have known that the plane was evacuated and that they would another chance to see Rachel. There was no reason for them to go.
When Ross decides to go after Rachel, Phoebe says her cab is right downstairs so she can take him to the airport. Why didn't Phoebe take Rachel to the airport?
Phoebe asks Ross if he's ever chased somebody through an airport before when he's going to tell Rachel he loves her. He replies sarcastically, implying 'no' but he actually did the same exact thing earlier in the series with Emily.
When Phoebe and Ross are buying tickets, there is a family of extras in line behind them. In the next scene, when Rachel is looking for her boarding pass, the same family of extras can be seen. Moments later, it is revealed that Ross and Rachel are at different airports.
When Phoebe tries to convince Rachel to get off the plane to give her and Ross time to get there, she claims there's something wrong with the "phalange". This is Phoebe's go-to fake word when making things up, and part of Phoebe's go-to fake name, Regina Phalange. Rachel treats this as Phoebe imagining things, but Rachel should have recognized the word and therefore the lie.
When Monica mentions that Ross had lived with their grandma while he was trying to make it as a dancer, Ross laments that they had gone 10 years without it coming up. However, that's just the length of the show/how long Rachel has been part of the group. The other 5 have been socializing together longer. Chandler & Joey were already living across the hall in the pilot, Monica and Phoebe have been established as previously living together (which is even mentioned during this conversation).