A comment by Todd Andersen got me thinking about the variety of factors that affect error rate in a molecular manufacturing system.
Todd is right that error checking of finished sub-blocks may be a way to reduce error rates. Whether this works depends on the details of the process. In some processes, it may be relatively easy to build a 100 atom part (of which maybe 98% will be perfect), then test and throw out the 2%, then stick the perfect parts together to make a perfect meta-part.
In other processes, an error will not only destroy the workpiece, but also the tool. So if a 10,000-atom tool is destroyed by each error, then the success rate needs to be 99.99% or better.
In a multi-stage process, each stage may have a different error rate for a different reason, and need different error handling. (Note that, unlike in chemistry, many kinds of errors can be corrected, reducing the eventual error rate.)
Tools that can only be built by molecular manufacturing may reduce the error rate drastically. For example, sorting rotor cascades can give you any purity you need, and atomically perfect sliding seals can exclude all contaminants. In that case, it may be a quick step from just barely good enough, to so good you don't even have to think about it.
A more general argument is that once you have general-purpose molecular manufacturing, you can probably build improved versions of your tools right away. So... although I can't prove that any given molecular manufacturing pathway will have a fast takeoff thanks to error rates crossing a threshold of significance, it does seem pretty likely.
This follows a general trend of argument: the difference between unfeasible and adequate is generally bigger than the difference between adequate and excellent. Feed "excellent" into an exponential growth equation, and you get a fast takeoff.
In future posts in this series, I'll be following this trend of argument in other areas, including range of machinery that can be built, size of design space that's accessible, and fabrication speed.