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Don,

There are two types of almanac errors to consider: errors of execution in the calculations, and errors in the predictive models. I have not seen any data on the former type of error, but Maskelyne was meticulous in his management of his computing teams, and he famously detected a conspiracy among them. The trick for avoiding errors in the execution of the calculation is really very simple: assign the task to two different people, working in absolute independence, and then compare. The odds of an error in the same number calculated by two independent, competent computers is very low. Unfortunately, this was piece-work, so the calculators had incentive to cheat. When Maskelyne detected such cheating, he modified his system and created greater assurances that the computers could not get together and share notes.

The errors in the predictive models of the Moon (especially) could not be fixed, but they were quite small (they had to be before the project could get approval). I hate to point to an old post, but I'm afraid I don't have time to write anything fresh this evening. Here's a post with a direct comparison of the old almanac tables and modern astronomical data. The "typical" error in the tables for the lunar distances, which were the primary data in the early almanacs, was around a quarter of a minute of arc on average.

Frank Reed