Building upon Mitchell's post below, I want to show another example of the dangers from within.
In 1992, Fr. Mitch Pacwa, S.J. published a book entitled Catholics and the New Age. The subtitle is: How Good People Are Being Drawn into Jungian Psychology, the Enneagram, and the Age of Aquarius. And he ought to know. The book is about how he was drawn into New Age teachings while he was studying to be a priest and after he was ordained. He finally saw through the mumbo jumbo and came to understand how dangerous these teachings are. The scariest part was that Catholic priests, religious, convents and liturgists were giving their assent, even encouragement, and in some cases, forcing the faithful to accept these teachings and practices.
There has always been danger and false teaching from within the Church; what better place for the Enemy to launch a campaign in the war against goodness, against God. However, we must stand firm and fight and shout out loud when we see abuses taking place. We must be vigilant in trying to see how the Enemy uses seemingly logical thinking to lead us astray. But it can be dangerous unless we are firmly grounded in our faith; unless we spend time in prayer, read the Bible (especially the Gospels) and become familiar with Church teaching such as the Catechism and papal encyclicals, we can be drawn away and perish.