When discussing scoring decisions about specific situations, we are making some assumptions about how each of the runners got to where they were on the bases, and how the inning ends. It always helps to clarify a few things, so here is an example...
There are two out, nobody on, and then three straight singles occur, loading the bases. The next batter strikes out, but the third strike is not caught, allowing the batter to reach first base safely, and allowing each of the other runners to advance one base, scoring one run. The next hitter flies out to end the inning.
Thus, the only reason that a run scored was the uncaught third strike.
If the scorer rules it was a passed ball, then the run is unearned (passed ball = catcher's fault).
If the scorer rules it was a wild pitch, then the run is earned (wild pitch = pitcher's fault).
Er, HotCornerDad, if the run scores solely because of a wild pitch (even without the strikeout), it IS an earned run.