I've read many of his books. I generally enjoyed them at the time (during my novus ordo days).
I caught him in a lie during the brouhaha of Mel Gibson's "The Passion". On Chris Matthews' show Fr. Greeley was talking about how unfaithful the movie was to the Bible and he stated that Our Lord forgave His crucifiers. Well, in the movie, Jesus asks God to forgive them three times. So, the portrayal had Our Lord giving even more forgiveness than is stated in Sacred Scripture. However, that wasn't Fr. Greeley's intent.
Fr. Greeley was committed to the new theology and the new ecclesiology of the novus ordo. So, he has to carry that with him to his Particular Judgement. He fully embraced the apostasy in all its facets although he did pretty it all up with some Catholic-looking window dressing.