With all the discussion about the Anglicans, we can't forget that there are other Christians whom Catholics have ecumenical dialogue with. One of the groups with a good sense of what ecumenism truly can be is the group Evangelicals and Catholics Together (ECT). While they are not an "official" group sponsored by the Catholic Church or any evangelical churches, they do important work in furthering the theological discussion.
Some who participate in ecumenism wrongly believe that unity is more important than truth, ECT does not. They start with an honest appreciation for dialogue, what each tradition holds as doctrine, the things held in common, and the things that divide. So, there is no false ecumenism in ECT where truth is put on the back burner. They sincerely want the same goal "that they all may be one" as Christ prays in John. But, not unity that sacrifices truth.
With all of that said, the newest statement by ECT has been put out.
It is on Mary and worth a read.