I choose a defensive approach for error handling at the time of implementation: only logged the problem (so that it can be fixed by changing Jira settings if needed), but did not make the job fail. My idea was to let the job do as much as it can. If for example no matching issues are found I considered that the job should not fail (for periodically running jobs it's likely to not find new issues at each run). I considered the same about an impossible transition. Maybe some issues are transitioned correctly others are not (depending on their corresponding workflow scheme).
Not sure if failing to update a single issue should fail the job or not.
I did not plan to fail the job for incorrect Jira config, only for incorrect Jenkins config. I agree that whether failing a job silently is a good idea or not is indeed debatable
Did I convince you? If you have some solid arguments we could change the behavior the way you suggested.