There is an OO manifesto (“Open orthodoxy! A modern Orthodox rabbi’s creed”) which is on-line and by itself seems fine to me. However, Some OO “rabbis” have crossed the line perhaps due to the influence of other groups on YCT. This has led to a push-back by rabbis such as Avraham Gordimer.
So far as I know from what I read on the Internet (I live in Israel) there is a difference in the shuls welcoming (apparently looking the other way) active (as opposed to celibate) gays and giving greater roles to women (e.g. aliyot, leading Kabbalat Shabbat). Hopefully they will take the criticism to heart and retreat a bit as did the Chassidim (according to the Tzemach Tzedek quoted in “Mekor Baruch” by Rabbi Baruch Epstein). According to Rav Kook this is the purpose of opposition to a new group.
I think that MO is a bit more traditional in synagogue practice although now there is also Centrist Orthodoxy and Morethodoxy. Maybe the list of subgroups will become so cumbersome that people will return to tzaddikim/benoni’im/resh’im (also Rav Kook’s view).