We have just start experimenting using Boinc to run a local grid for one specific application which involves a numeric search for a solution. If an appropriate solution is found, it might mean that no further tasks need to be executed for that job.

What is the recommended way for the assimilator to cancel all remaining tasks for that job if it finds a solution that eliminates the need for further searching? And, is there a way to notify the clients to cancel any tasks they might have queued up?

Try https://boinc.berkeley.edu/trac/wiki/CancelJobs

Well, that makes me feel silly. One follow on questions: is there any bad side effect to calling cancel on workunits that have already been assimilated or do I need to take care and only call it on those that have not been returned yet?

I don't think so, but that one's a bit above my pay-grade: my experience is more as a client-user than as a server-administrator.

I would say that cancelling test jobs in a closed test environment has very few downsides, but is something to be avoided in a live environment if at all possible. Sometimes the BOINC system cancels jobs issued to clients if they haven't started running yet - say if a late return from a wingmate completes validation on the workunit. That's not a problem - nothing is wasted.

But if you cancel a job which has already started running, then the time spent so far IS wasted, and your volunteer users might start to feel that their efforts aren't being valued, and start to drift away.