The thing about showing the others what was said in the diary room is that it would only work once. After that you'd get them being really nice and also you'd lose a lot of the bitching we see in the Diary room as they wouldn't risk it being shown. Would be hilarious though especially after a couple of weeks (when they think they have made alliances etc, who cares what they say at the start)
I certainly think the idea that an evicted HM will make a nomination or even 2-3 people for the week after they leave would be interesting.
Theres also using the result of a skill test (or group of tests) to determine nominees.
But personally I like the idea of making it linked to something silly, like those who slept most (and therefore contributed least to the house) or the ones who did the least cooking or cleaning. And do this for after the fact, might also make them do more stuff in the following weeks just in case.