If it were possible to prevent fraud with very good certainty, I don't think it'd be that bad of an idea. It would save a lot of money if a person wouldn't have to run a re-election campaign at the end of a set term if the person would have obviously been re-elected.
Good point about obvious re-elections being a waste of money. Ironically the first quibble about this plan is going to come from me. 
Petitions aren't secret ( you have to out your name on them) so a bad ass government could make things hard for the signatories.
But then again it depends on the political climate of the country. if its open to dissent then there is no problem, but its no good for a place like Iran.
Possibly, but if you think about it, if people saw that the signatories were being treated badly, the government would not exactly have that high a chance of being re-elected.
