I'd describe the most important on-page factor as "focused, quality content". Focus is essential to establish clear relevance signals rather than ambiguity.
"Quality" matters not only because the Panda algorithm attempts to measure quality directly, but also because that's what it takes to attract "freely given, editorial backlinks" - and that's the off-page factor that is coming into play most powerfully.
More than ever, looking for just a couple of angles that will do the trick is becoming unwise. It takes a rather holistic, all-araound approach to get rankings and generate engagement with your visitors. (I suppose you could say that engagement is an on-page factor, but really it's more like on-site.)
these are links to your content that are entirely unsolicited, that other websites give to you because your content is in their opinion worthwhile - these are obviously the best links you can get and you get them by creating content that others might find interesting one way or another.