I was a scrutineer for one of the parties at one of the polls in the riding I lived in during the last federal election in Canada. There were two other parties at the poll who had scrutineers. Each of the three of us sat around a table while the deputy returning officer counted each ballot, showed it to the scrutineers, and waited for the scrutineers to not any exceptions. When he was done, the ballots were sealed in envelopes (which the scrutineers were permitted to initial on the seal), and placed in a box for delivery to Elections Canada.
At the end, each scrutineer checked their count against the official count by the deputy returning officer. The vote total was checked against the ballot booklets. All counts were consistent with each other, and the total consistent with the number of ballots cast.
In this polling station there were no irregular or spoiled ballots, and we had a count to report to our candidate HQ, and for the deputy returning officer to report to Elections Canada, in less than a half hour after the polls closed.
There's no need for machines to count votes. And the notion that people can't count votes quickly, and accurately is pure bullshit.