1. The media is able to be tricked easily into believing something and then project that to the whole world.
At least twice in the movie someone was killed and the media twisted it in order to cover for the Vatican. Or, perhaps more accurately, the Vatican released an official statement about the incident and the media ran with it. The movie showed at least 4 different languages represented in the media, covering much of the world who would be eating up this lie. I am not sure if this was a major point they were trying to get across but I know I saw it as pretty important. We can indeed be fed a good deal of important information from media outlets such as TV, internet, radio, and newspapers (does anyone read those anymore?), but they can easily be twisted or lied to (or do the lying themselves) and it suddenly gets received as absolute truth. A dangerous concept in real life to be sure.
2. There was a strong sense that passionate belief in something does no make it true or right.
Towards the end of the movie a major decision was about to be made, something that would change the course of the Catholic church. The cardinals were conversing and becoming convinced of something and one of them said that if the Holy Spirit is leading them to do __________ (I won't give it away), they should do it because it is God's will. Come to find out that they were wrong and evidence showed just moments later. The point here is that passionate belief about anything can be misled. Even cloaking it around words like "Holy Spirit" and "God's will" doesn't make someone less susceptible to being fooled. We need to seek wise counsel, rely on God's leading (just because we could be led astray doesn't mean we always will be), and take a humble and patient approach to big decisions. Only God is perfect, and while we can make wise decisions it is best to do so slowly and with more prayer than we normally think is necessary.
Just some thoughts from a decent movie draped in Catholic mystery.