When the newly-elected Pope John Paul II is changing into his white papal cassock, the actor playing the pope switches between Cary Elwes and Jon Voight several times between shots (most likely this scene was filmed twice, once with Elwes and once with Voight, and the scenes were then edited together).
After Wojtyla accepts the papal election, the cardinals rise and applaud. The camera then pans in towards the new Pope. However, if you look closely, it is actually the mirror image shot from the previous conclave, with John Paul I clearly in the middle of it all instead of John Paul II.
When John Paul gives the Urbi et Orbi blessing after he is elected, there are 16 people standing on the balcony of St. Peter's Basilica. But in the following wide shot from St. Peter's Square, only two people can be seen on the balcony.