Maybe they just need to put up webcams outside the polling place to count how many people actually enter and then compare it to the election day vote totals from that location.
I think the webcam idea is a great idea.
I also think all electronic voting should give the voter a printed receipt that shows their timestamped vote, and a paper copy of that receipt should be kept by the machine.
That way there is a paper log that can be used to challenge the machine totals. And the web camera can be used to confirm that the number of people is accurate.