But this is a good question that Meta Tron is interested in getting at. So far, no one seems to have found anything about the WBC that is unusual in a doctrinal way. Yes, you can say that Christians shouldn't be hateful, etc. but that's talk about behavior, not doctrine.
Maybe the lesson here is that one's doctrine is not so easily separated from the practice of one's faith...
In any case, it is a hard question to answer simply because the church makes very few public statements about what it is they actually believe. We know that they are five point Calvinists, because they have said that much. We know that they are against homosexuality, because of their protests.
They have also made statements that they believe funerals are necromatic rituals in which people "worship the dead." This point particularly seems in contrast to orthodox Christianity as most Christians do not believe that having a funeral = worshiping the dead. We also see no condemnation of funerals in Scripture - in fact, Jesus is recorded to have attended at least one (that of Lazarus), though in that case it ended up not being a funeral after all. I'd be interested to know if they hold funerals for their own dead. I know that they at least bury them in the regular cemetery and put up tombstones for them.
Some of the other stuff that they have said... like, in documentaries and interviews, seems very off. But they don't go into great detail on their minute doctrines, which is how they can appear to have orthodox doctrine while practicing hate. I'm pretty sure that if someone was able to really dig deeply into it, they'd find out that there are some rather stark departures.
They are an apocalyptic cult, from what I have seen. When Louis Theroux interviewed them last time, some of the kids told him this elaborate story about how one of them had a dream about the family hiding in pink caves, and then they found out that there really are pink caves in Israel. And they gave him this very detailed account of what they think is going to happen in US politics regarding their court case that was before the Supreme Court at the time. Like, they said the Supreme Court would uphold their rights, but the US people would hate it so much that they would revolt, causing the President to transport the Phelps family out of the US via Air Force One, and they would end up hiding in pink caves in Israel while the rest of the world went to hell in a hand basket, and then Jesus came back. Obviously, their prediction did not go as planned.
So - if that's just a taste of what they come up with, I'm willing to bet that behind closed doors, there's a lot more to the story of their doctrine than the rest of us will ever know. And we'll be better off for not knowing it, in my opinion.
Granted, they aren't the only group to have come up with whacky end time prophecies... but such beliefs are not orthodox, regardless of what group cooks them up.