Interesting video, and he makes a few good points.
1) Sodom story isn't about homosexuality, so he's right on that one.
2) Leviticus- harder to get around that one. His argument there is weak, and he makes a supersessionist argument (which is really problematic).
3) Romans- As I've said before, Paul wasn't talking about sexual orientation, so his point remains.
4) Cor and Tim- Again, the word study is a real issue because it's not as clear at our English translations don't get at the issue.
I didn't think the video was that great- and if I didn't agree with his conclusion, I don't think it would come close to swaying me. From what I can tell, he's not a Biblical scholar, nor does he have any formal training in Biblical studies, Hebrew, Greek, or exegesis. Not to say he doesn't, but I couldn't find any reference to it. And that's also not to say that only professionals with degrees have a right to have an opinion on the matter, but if you're going to be the "face" of the movement, credentials are important.
So, for me, here's what it comes down to:
OT references are legit, it's fairly black and white. Same sex intercourse is bad. Nothing in there about same sex relations, as those didn't exist in the sense that they do today. But there's no "explaining away" what it says in Lev.
NT references are problematic due to the words used and the wide range of interpretations.
But it's a bigger question than Scripture, but rather about hermeneutics and systematic theology- which these promo videos (on both sides) are lacking. Like it or not, the Bible is not inerrant, nor is it the Word of God (that's Jesus. You can say that the Bible is the word of God, but not the "W"ord of God). Furthermore, the Bible has been used to support a lot of negative things that actually go against the spirit of Scripture, while other parts of it are ignored. It's nearly impossible to make any argument (with apologies to Luther) on the basis of
sola scriptura. Reason (and common sense) as well as tradition (both of the Church, but also personal experience) is vital in this conversation. And that's where I think the room to embrace same-sex ordination/adoptions/ordinations/rights comes from. The Bible should point us to the grandeur/mystery/majesty of God, not reduce God to an answer. The problem is that we're using the Bible as a microscope instead of a telescope.
The question isn't "what does the Bible say?" That's the wrong place to start. The question is "what is God's will/what is God calling us towards." The Bible is a part of that answer, but it is not THE answer. The Holy Spirit has guided the Church in the past, so to say that the Holy Spirit can't lead us to a new understanding of sexual identity and relations is actually more blasphemous than saying that the Bible isn't the final authority on the text.