Any remade punchcard should be witnessed and approved by someone non-partisan.
In neither case should the ballot be "remade". Voter error, first of all, is the voter's fault; the voter was instructed on how to create a legal vote, and failed.
As for machine error, it is known in advance that these machines have some error rate. We consider this error rate acceptable, and voters are willing to live with that risk of error, otherwise we wouldn't have collectively decided to use the machines in the first place. (If we are unwilling to live with that error rate we ought to switch technologies; I suggest hand-marked and hand-counted paper ballots.)
In close elections (i.e. Florida 2000) it may or may not be necessary to hand-count the ballots which were rejected due to machine error (not the ones rejected due to voter error however). But this wouldn't involve "re-making" ballots either; it would involve counting (or deciding they are non-votes e.g. if the chad is merely dimpled) the existing rejected ballots. In that case, a hanging chad for Kerry, with no other President chad missing, goes for Kerry, sure. But this would be done by hand, by the election board. Also, since machine-error rate is likely to be randomly distributed to voters for either candidate, *fully* recounting rejected ballots is usually not called for. Only if some *partial* hand recount (or "canvass") shows a huge bias one way or the other, or if the race is extremely tight, can it make sense (depending on the state's election laws).
I just can't think of any justifiable reason to ever "re-make" a ballot under normal conditions.
The election inspectors followed the "two corner" rule. If there was a 'hanging chad', they showed the head election supervisor for a 2nd opinion, then showd me and the dem challenger for third opinions while we watched to make sure the vote totals matched.
We got our butts kicked in EL like normal, but it was legit.