We looked like a damn Banana Republic in the 2000 election.  And there is certainly legitimate reason to be concerned that the folks who were running the elections in Florida, on BOTH sides, cared MORE about who won than about making sure that the process was beyond reproach.  A strong case could be made for taking the process out of the control of anyone who has a partisan stake in the result.  For example, an accounting firm, who was subject to audits and challenges from both sides and would need to prove the robustness and accuracy of their results, would be a better solution than what we have now.

And maybe bring in international observers, under the auspices of either the U.N. or the World Court, who's job it is to report back to the international community that the election was fair.
We often demand this of other nations.  In 2000, we proved that we are no better than the other nations of whom we demand this.  I certainly would feel better about the U.N. being the arbiter of our elections than I do about Jeb Bush, or Antonin Scalia being the arbiter, as we KNOW that they are biased toward one side.