I freely admit that there has been for a short span of time a goodly interest in this topic by pretty much only the British Fourth Estate. If multiple heads roll at the Beeb, I will grant you the point, but if it is just confined to one scape goat, as was done in the Andrew Gilligan scandal, then I will say that it is cover-up as usual.
Probably it's only died down at the moment because there's nothing much new emerging -- I think there are still various enquiries underway, as well as Operation Yewtree, and once something comes out of all that it'll be thrust back into the limelight. (Although as an aside, a cynic might suggest that certain segments of the press found the scandal very useful indeed, as it distracted attention from the then-ongoing Leveson Inquiry into their own conduct!)
However, I believe there's already been more fallout than just the resignation of the previous Director General; from memory the editor of Newsnight (who spiked that programme's investigation into the allegations surrounding Saville, and perhaps green-lit the atrocious piece on 'a prominent Conservative minister in Thatcher's cabinet' with some measure of 'we won't get caught napping again!' in mind) and the overall head of News have been given the shove. That's not to say that that should be the end of it, of course, but I think on balance it's generally better to work out exactly whose heads should be placed on sticks, rather than calling for arbitrary beheadings and inviting yet another round of tiresome self-flagellation instead of addressing whatever root problems may exist.
On the other hand, criticising the BBC is all well and good (it's almost the national sport, after all), but to my mind there are plenty of other serious issues raised by the whole Saville thing that have nothing to do with the BBC's (in)actions. For instance, seven different police forces appear to have received a total of 31 allegations of rape between them, and it seems they did utterly sod all about them; the media at large also appear to have had more than an inkling about his activities and yet made very little attempt to do anything with the information until recently. Not to defend the BBC in this case at all, but it's a scandal that reaches far beyond their walls.
No government should have a broadcasting arm that purports to report objectively on policy matters.
The BBC is, in theory, editorially independent of the government -- to what extent that is actually true might be the subject of some debate, but if it were intended to be the government's spin machine it would appear to do a bloody poor job of it. The governance model has the BBC Trust holding responsibility for operational oversight and editorial standards (not editorial direction!), and as I understand it the government can only recommend appointments of Trustees rather than exert direct control over any editorial or operational staff.
I'm not sure what overall effect the Gilligan affair had on the BBC's editorial policies, but the Hutton Inquiry into that mess would be the most blatant (public) example I can recall of the government of the day trying to have an obvious pull at the Corporation's strings. For what it's worth, the immediate results of that inquiry were actually three 'resignations' (Gilligan himself, the Director General, and the chairman of the Board of Governors -- the governing body that was later replaced by the Trust, and had the same general relationship and responsibility to both government and the BBC.)