It's established that there are 108 cardinals involved in the conclave. However, in the third round of voting there are a total of 110 votes and then in the fifth round of voting there are 113 total votes counted.
In one scene, Cardinal Bellini states that he is the second most senior Cardinal. However, his seating placement contradicts this claim, as he is shown seated far from Cardinal Lawrence, the most senior Cardinal. In reality, Cardinals are seated in the Conclave according to their seniority, making this an inconsistency in the film.
Before zipping the shroud of the deceased Pope, his jaw would have been lightly yet snuggly bound with gauze and tied to the top of his head. This would be to prevent the jaw from dropping open as rigor mortis sets in, thereby making his final facial appearance difficult to ultimately achieve.
In the movie, the seating arrangements during the Conclave are depicted incorrectly. Traditionally, the Dean of the College of Cardinals, as the most senior Cardinal, is seated at the beginning of the first table on the left (on its right side). However, in the film, the Dean is shown seated at the end of the table (its left side), which is inconsistent with the actual protocol.
It is claimed there was a visa application to Switzerland for the Mexican cardinal to go to the hospital. However, Mexican citizens do not need a visa to enter Switzerland.
In the film, Cardinal Lawrence is shown preaching to the College of Cardinals in a room before the Conclave. However, in reality, this sermon is traditionally delivered by the Dean during the "Missa Pro Eligendo Pontifice" (Mass for the Election of the Pope), which is held in St. Peter's Basilica.
An archbishop claiming to have been made a cardinal "in pectore", but whose name was never published, is admitted into the conclave. However papal law states that all "in pectore" appointments made by a pope expire with that pope's death if the appointment was never published. This is to prevent people from making false claims of "in pectore" appointment like Cardinal Lawrence suspected at first, but was convinced by a document the archbishop had with the pope's seal. However there have been numerous cases throughout history in real life of forgeries made of a pope's seal, which is why documents pertaining to an "in pectore" appointment are rendered invalid after a pope's death if the pope himself never publicly announced and published the document. Yet Lawrence makes a minor reference to this rule having been changed just recently in the laws of the Holy See of the universe of this movie.
It is stated that Adeyemi would be the first African Pope. The Roman Catholic Church has had three African popes: Victor I, Miltiades and Gelasius I, all prior to AD 500. It is however likely that he means the first Black African / Sub-Saharan pope, as those three popes, while born in Roman Africa were all of North African and/or Roman or Greek ancestry.
Priests are not allowed to disclose anything they hear in confession. Even Dean Lawrence mentions it himself, but then he seemingly violates the seal by talking about the nun's confession with cardinal Adeyemi. Yet if you pay close attention, Lawrence never reveals any details at all, and mostly just leads Adeyemi to reveal all the details himself.
Cardinal Benitez delivers his climactic speech in Spanish. All of the Cardinals speak fluent Latin, and many have conversations in Italian. Spanish and Italian are both derived from Latin, so the Cardinals could have a basic understanding of Spanish.
There's an audible "thud" when the ambulance crew drops the pope's body onto the gurney. A crew would presumably show much more care and reverence when transporting a deceased pope, yet it might also be symbolic and reference that humans all enter and leave the world in the same way, pope or pauper.
At around the the 17 min mark when Lawrence is talking to Wozniak, you can see Wozniak mouthing the words that Lawrence is saying.
Cardinal Lawrence says to Cardinal Tremblay "you would libel the Holy Father in his own home?" In fact, it is not libel which is a written form of defamation; rather, it is slander, the spoken form of defamation.