(Written in response to Tony Hirst. I don't know why I went into such detail; maybe it's because I think it's actually a pretty good system and wanted people to know how it works.)
Interesting. In Canada this is done quite differently. Each political party is allowed a scrutineer at each poll (a polling place, like a school gym or church hall will typically have 5 to 8 polls, and often a single scrutineer will handle all of them, but the number of scrutineers increases as the polling place gets busy).
Each poll is basically a table with the poll number on it. A poll may be an apartment building, a few city blocks - usually a few hundred voters. The poll clerk, who is hired by Elections Canada, and is neutral, has a list of electors - their names and addresses within the polling place. This list is created ahead of the vote by enumerators who go around knocking on doors and finding out who lives there.
This voters list is public information. It used to actually be stapled to telephone poles in the poll, but now you have to go ask for it. So each scrutineer also has a copy of the voters list (and, of course, they have master voters lists in the party office, correlated with their own lists of people).
The scrutineers sit right beside the clerk at the table. When the voter comes to vote, the scrutineer will hand them a signed and numbered ballot, then cross out or check their name, to indicate that they've voted (the voter may be asked to produce identification or present their voter's card they've been given by the enumerator).
(If your name is not on the list, then you need to produce something with your address and your name on it to prove you live in the poll, and swear (or solemnly affirm, if you're not religious) that you are who you say you are, and your name will be added to the list. The demand for identification is a formality; in fact, a person's word will be accepted at the poll. It's rare enough that any attempt to vote twice would be caught.)
The voter goes to the little cardboard shelter on another table (our entire electoral system is made up of folding-leg tables, cardboard boxes, and paper ballots). He votes and folds up the ballot. Once he returns, the scrutineer checks the number, detaches it from the ballot, puts the now anonymous ballot into the box, and stores the number.
Meanwhile, the scrutineers then cross out the voter's name on their lists, indicating that the person has voted. Runners from the political parties come in and out of the polling place to collect the sheets. Back at the party office, more workers call our otherwise round up supporters who haven't voted yet.
I've taken part in this process half a dozen times or more, as both an inside scrutineer and an outside scrutineer (runner). It is an enormously satisfying process to work in the polling place all day, to see every elector come through the hall and vote, to look at their faces, to see the cross section of a community. Polling places are always happy, uplifting places, even when the parties are bitterly opposed (there's some back and forth, but the scrutineers from different parties don't really interact, but they're not hostile to each other either).
I suppose this could be automated more - both the voting process and the scrutineer process - but I'm not sure I would want it to be. I like the fact that when you vote you are a person, not a number. I like the fact that you leave a permanent record of your vote in the ballot box. I like the fact that it takes a certain amount of effort to scrutinize an election, but at the same time that you are able to directly observe every part of the process except the actual printing of the 'x' on the ballot.
(Scrutineers remain present in the room during the counting process; for each poll, the poll clerk and the assistant poll clerk open the box and count the ballots right away, in full view of all scrutineers in the room. The number of ballots in the box must match the number of ballot numbers that have been turn off the ballots, which in turn must match the number of voters on the voters list. The tally usually takes up to an hour to produce (it takes longer if a ballot has been dropped on the floor or if a mistake was made with the voter's list (but everything you need to spot the mistakes is right there)).
I suppose now the way to do it is to give the outside scrutineer an iPad with web access to the party's central voter's list, and have him or her simply check off the names as people vote. That wouldn't be too difficult to set up, and it would feed right into the list of known supporters in the poll.
More automation than that would introduce an unwelcome layer of obscurity into the process, and make the system less reliable.