Probably sometime between when Erlang was developed and the first MapReduce paper was written. There isn't "One True Way", but there are plenty of solutions.

We don't need to re-invent MapReduce or message passing. There are ready made solutions/frameworks like Hadoop and Storm that are fairly easy to implement. There are also a number of databases that are designed for distributed computing. You don't need to be Google to have a fault-tolerant distributed computing setup. It's really a matter of choosing the appropriate technologies, rather than re-inventing the wheel. Because of that, I'd consider it a "solved" problem, even if a particular implementation might need some thought to match up with appropriate technologies. It's not necessarily trivial, but it's probably as "solved" as it needs to be.

How many of those issues go away with infinite storage, atomic storage operations of arbitrary length, instantaneous computation and communication, completely deterministic executions of operations, completely reliable machines, etc.?

My point was more that the parent posts examples were problems that really are more engineering than theoretical in nature.