Rachel could not have used the airline ticket to Athens as it would have been in Emily's name, and a last-second change of passenger name at the gate would never be permitted under security regulations.
On the flight back from London to New York the direction on the monitor in front of the seats is wrong. The little plane on the screen is going from left to right indicating that the flight is actually going from New York to London. It should be from right to left. You can clearly see it when Joey is talking to Chandler.
Even if they could have transferred Emily's ticket to Rachel, she couldn't have gone to Greece as Greece requires US citizens to have a visa.
Emily never said her vows to Ross. Correction: This is a continuation of the season 4 finale. Emily said her vows in that episode, Ross only re-said his vows in this one because he said the wrong name as a cliff-hanger for the season finale.
(at around 4 mins) While Phoebe is talking on the phone, the fake building background outside the window can be seen moving around.
At the airport with Ross, 'Emily' is revealed to be played by a body double when she turns around to leave and the double's face is visible for a split second. Helen Baxendale was only shown in close-ups, which were evidently filmed separately from the rest of the scene.
In the very beginning, when a wide shot of the wedding is shown, it's possible to see the end of the set in the right corner.
(at around 11 mins) when Chandler is talking to Ross and says "for about 30 minutes", his mouth is clearly not saying those words.
There is a shot in the living room area of honeymoon suite of Ross and Emily's mother where the edge of the wall is visible on the right side of the screen and you can see into the bedroom.