I suspect what people perceive as the dominant issue will vary depending on their circumstances.
So, for example, ordination of women is one I probably have to spend the most time thinking and talking about, but the reason for that is obvious. Someone whose job is to chair an ecumenical body will clearly spend more time on that issue.
I agree with what mkgal1 said, and I'd add that I think one of the biggest issues is how one integrates Christian faith with other fields of knowledge. I think a "liberal/moderate" is more willing to have a sense of faith which is integrated with the various sciences and so forth, and a "conservative/traditional" is more willing to reject other fields of knowledge in favour of a "pure" faith.