It's not that simple
It should be easy to make electronic voting systems which give better, more verifiable audit than UK-type paper systems: indeed, that's kind of what this article is about. Some of the voting systems used to elect Bush in '04 gave no audit at all, and stored their data in an Access database.. IMHO, whoever signed off on those systems ought to have been fired (but as that would have probably included the President's brother, it's not entirely surprising that didn't happen).
But..
One of the main drives in turning voting to electronic over paper-based systems is counting efficiency; the other is trying to make voting "easier" as turnouts fall. What doesn't seem to have been realized is that the easier voting gets, the fewer people vote: look at Afghanistan - serious risk of being bombed/gunned down in the long polling station queues, and they get a turnout in excess of 90%.
That's what we should do: have random attack squads with machine guns & IEDs hitting random polling stations - put a real sense of fear into people so they'll get a real adrenaline rush from voting. Have assault courses or minefields that need to be traversed to get to the polling booth.. make people work to cast a vote.
What could go wrong?