Wilburforce - 12:25 pm on Dec 19, 2012 (gmt 0)
Anything that could help us work out what we could have done wrong.
I wouldn't start with assumption that we have done anything wrong.
There are clearly multiple factors in play, and their interaction is currently throwing up a lot of anomalies, including massive drops for perfectly sound pages, and thin pages/sites coming up on page 1.
The only clearly visible factor is that in general (but not universally), the top positions compared to a year or so ago have lower keyword density/count, and lower PR (according to Opera's PR tool). Coupled with odd synonym spikes, this suggests that Google is placing much less weight on keywords in both backlink profile and on-page, and is giving more weight to synonyms. To paraphrase Tom Sharpe, you should never be afraid to call a spade an earth-inverting horticultural implement.
Heavy keyword use may cross some threshold and incur a penalty, but changing internal links and/or on-page keyword count and density is only really appropriate if the keyword use was inapproriate in the first place.
As an example, I have one particular (non-commercial) page about a technical subject that is well-regarded in a relatively narrow technical field. It has a lot of unsolicited backinks (most of which have technicalsubject as the anchor-text), as well as a lot of sub-headings like technicalsubject calculations, technicalsubject applications, etc.
There isn't anything "wrong" with the page or the backlinks, but in May it fell from the top of Google's page 1 (where it had been for years) to nowhere. I'm not going to change content that makes obvious sense on the page (and e.g. SI units don't have synonyms), or contact a lot of third parties to tell them to change the "water" anchor-text on their page about water to "H2O". Consequently, that page (still at the top of page 1 on Bing) will probably never return to Google's page 1.
We should all be clear that some of Google's changes in the last year have produced ridiculous effects, and trying to fix these ourselves is an Emperor's New Clothes reaction.