I've just finished translating the late Fr. Jean Galot, SJ's article on the role of private apparitions in the life of the Church and in salvation history. It has a good section with principles of discernment and an explanation of why Church approval of an apparition is never an infallible judgment. An excerpt:
Often apparitions have been received with a passionate enthusiasm, and have made crowds of faithful rush to the place where they have occurred. In effect, many expect to find a confirmation of their faith in those who "see". This favorable prejudice could easily encourage a credulity that does not really seek to test the signs of authenticity of the phenomenon.
Others, in contrast, assume in regard to apparitions an attitude of scepticism that closes them to any judicious examination of the facts stated. Sometimes this scepticism touches their faith itself, because it is from a lack of faith that some reject all sensible manifestations of the supernatural. In other cases scepticism is simply that of the believer who wants to hold to the faith as given and feels repugnance in the face of something that seems to introduce elements of vision.