The most obvious one that comes to mind is the entire Hell doctrine. Once this heresy is understood, there isn't a clear statement of scripture that can be held true while also believing in eternal torment. The letters to Hagee and Kennedy should give you quite a good list.
It could well be said that the concept of free-will and the concept of the total sovereignty of God (including and especially His Foreknowledge) are also doublethink, though I don't believe that BOTH can be fully held and believed in the mind at the same time without 'blurring' the meanings of one or both. That would make this less doublethink and more 'less-than-perfect' understanding at best, and dishonesty at worst
One of Ray's gifts as a teacher is in hunting down 'apparent' contradictions in the scripture. There is a related word, though not identical in meaning, Paradox that Wiki partially defines "A paradox is a true statement or group of statements that leads to a contradiction or a situation which defies intuition;..." . Just by that definition, the scripture contains numerous 'paradoxes'. Die to live is a powerful one.
Of course, we know that even Christian denominations cannot agree on even major matters between themselves. So if you are talking about doublethink in Christendom's Theology in overview, it is chock full of contradictions, another related but not identical word.
It's been a long time since Philosophy 101, so I hope I haven't muddied the waters too much.