1) I don't think it's relevant to the debate here. The rise in real wages, as adjusted by the CPI, started in 1996. But no changes were made to the CPI until 1999. So it cannot be that "Clinton's changes in the CPI" accounted for the rise in measured real wages that began in 1996.
2) The main change was 'geometric weighting,' which was not exactly Clinton's idea. This article talks about all the people who were screaming one way or the other about this. Basically it comes down to...
So this is one of those "angels on the head of a pin" arguments among economists, with political forces on either side trotting out whichever "experts" will say what they want said.
To label these changes as "Clinton's" as a way of denigrating them is more rhetorical than useful. There were plenty of people with excellent credentials saying that the changes were warranted.
3) I don't think it makes much difference. The CPI in the post-change world is but half a point away from where it would have been under the old scheme. My view of all these things is that if humans get within one percentage point of the truth, it's a miracle. Any slop that's less than a whole point is probably swamped by other effects that are inherent in human fallibility.
Wouldn't it also exaggerate any current increase in real wages? Would there be any increase in real wages in the past year if the CPI was computed under the old system?