I don't think he did it or that we are meant to think that he did, otherwise we wouldn't have learned from the mom that the black kid was gay, the initial doubts that Sister Aloysius has about Father Flynn were so spurious (that he touched the kids hands cause his fingernails were so dirty). Ultimately, though there is plenty of circumstantial stuff that wasn't answered beyond a shadow of a doubt, which I think is the point.
I took the end w/ her doubts to have a few intended reasons they want us to think of. Firstly of the grander theme of the movie: Aloysius is in doubt of the future of the church because of the reforms of the new pope who was here represented by Flynn (I saw allusion to this when she tells Sister James to put up the picture of the pope so the kids think she has eyes on the back of her head; and she asks him somethin to the effect that shouldn't she put up a picture of the living pope?). Also, I thought she had some doubts about her certainty of his guilt, and finally that her certainty itself is doubt.