Abortion. This is the #1 topic. The Christians who argue pro-life inevitably boil it down to the following points:
A: 'Every sperm is sacred' - they claim the fetus is 'alive' from the moment of conception; Doctors disagree.
B: 'The USA is a Christian nation' - they claim that since the USA is a 'democracy', then mob rule is in effect, and they can force their religious values on everyone/anyone else; (This is tricky to change their thinking on. It is ingrained and sub-concious, and certainly seems to be the direction we are heading towards.)
C: Their opinions on medical issues, especially other people's medical issues, have more legal weight (because of mob rule/'democracy') than that of a licensed, educated, trained physician in posession of the facts of each case.
The South Dakota case makes it a bit more complicated, and I haven't done any research into that yet, but the trolls certainly do gloat over it, especially the ones who imagine that we have the rule of the mob instead of the rule of law. I know the strategy they are trying to use, here and otherwise, is to ensconce their religious views in law without overt reference to their religion.
OMGawth this is ENORMOUS. talk.origins archives has tonnes of information, but the best 'quick' education on the whole topic can be gotten by reading the Kitzmiller vs Dover School District decision. It all boils down to this:
The "God of the Gaps" argument. To whit - "There's this phenomenon that hasn't been explained by / seems improbable to be explained by / I can't imagine how it might be explained by - science, so our Deity did it." Which is really the willingness to assign a value without backing data (which is bad science), and Pascal's Wager - which begs the question of the existence of their deity. Behe's a poor scientist and has popularly published pseudo-science.
The trolls will claim there is no evidence for evolution. Laugh and point them at talk.origins, mention morphology relationship trees and DNA relationship trees, and then dismiss. They will weasel 'theory'. That should be nipped cold dead immediately.
Atheists are Satanists/evil/amoral.
This is ad hominem disguised. The biggest sticking point of them all is the assertion that 'rational morality is relative', and is therefore somehow inferior because it is not 'absolute'. Their morality, they do claim, is 'absolute' because it is 'divine' and 'unchanging'. I have a lot of issues with /that/, on many levels. It's probably the biggest thing that needs to be addressed and changed amongst atheists and other people with a naturalistic worldview - making an easily understood case for, and making people aware of, the fact that people aren't evil and are capable of having functional, useful, good sets of naturalistic morals (without having them be dictated by a 'deity' or the "deity's prophet"). I think I ought to try and get with some people on TheBrights.net and work something out.
Atheist/Gay/Satanist "agenda to destroy America". Fun, fun, fun, never-ending morass of ad hominem. Normally pointless to engage these folks except to build chops.
"The United States is a Christian Nation".
Theist, Please. This is my favourite easy-to-debunk bit. Most of the founding fathers were Deist, most hated organised religion and the body of organised Christianity of the time, freedom of religion means freedom from religion (I love that court opinion, too), official documents make it clear that we are a secular nation, and the Declaration of Independence (while it is a very influential document in the history of the United States) is not an official document of the United States Government - so the use of a Latin turn-of-phrase in it doesn't matter. Throw some Federalist Papers at them.
"The bible is factual history."
See, I know some, but not a great deal, about the actual Bible itself. I read through it once. I was annoyed by it. Other people have done enough work on the Bible itself, and every faction of Christianity argues with every other one on how to interpret almost every line. Counter that with Skeptic's Annotated Bible, and they might as well tar-and-feather themselves. I know it's not 100% literal, factual history.
This is a subset of the one immediately above. Which of the FIVE different creation stories in Genesis are they referring to? Most have never read it throughly enough to realise that there are conflicts in the story.
"Dr. Dino / Kent Hovind ..."
Theist, please. It is to laugh. He got his 'doctorate' in 'Christian Education' from an unrecognised diploma mill in a split-level home in the MidWest, for a dissertation that is unpublished, far less substantial than what he claims, contains rambling narrative, unoriginal work, almost no references, spelling, grammar, usage and punctuational horrors and non-sequitur structure - which he also suppresses anyone from actually reading. He's been indicted for tax fraud wherein he claimed that he was bankrupt, whilst proffering a large sum of money he doesn't have to anyone who can change his mind about evolution on his own terms, which happen to be weasel-terms. He 'debates' in order to kick the other person in their lack of specialty and fails to correct factual errors and re-uses rhetoric that has been widely debunked. He is bad faith personified.
I've done some research on Answers In Genesis and Institute for Creation Research. AIG, for a very long time, had a motto on their front page of their website, declaiming that everything they did was done to support the literal truth of the Bible - which is a patent admission that nothing they publish is capable of being scientifically sound. They both cherry-pick data, they both ignore inconvenient facts. They are both widely plagiarised and cited as 'scientific sources'. They're not, and that train of debate should be stopped cold immediately - nothing they publish is science. Bad faith peddlers.
Heim-Droescher. Heim was a physicist that, in the Fifties, came up with an obscure and difficult-to-understand method of describing the universe - and it's now gaining popularity and research. It is immensely advanced mathematics, and might generate good science or might generate pseudo-science. The problem here is that some of Heim's later work starts to talk about 'organisation', 'spirit', psychology, etc. seemingly speaking to an 'intelligent designer' - and I'm certain that some of the ICR/AIG/ID people are going to start making grabs at Heim theory just because it might be so difficult to authoritatively de-bunk it, and hey - it's physics, right? Science proves ID! grarh.