Voters would enter their vote into a computer. The computer would print out a card for you, and show it to you from behind a perspex card. You would then say "OK" to verify that it was correct and it would drop into a box.
Now there'd be a physical copy of the cards. These could be counted and checked by scrutineers as the current electoral process works. They would need to do a manual count independent of the electronic count, and the judiciary could oversee a wrap-up ceremony where the two were compared for correctness.
In order to rig a vote and get away with it, you'd need to hack both the computer system and the manual count. Chavez could do it, but joe random hacker definitely couldn't.
But you'd get a fast, clear result for television purposes. Voting cards would not be ambiguously filled in the way they are now. And if you had a compulsory preferential system, as in some jurisdictions now, you could cause the software to enforce that in a way that isn't possible with manual entry at the moment.