Which small spot on this hot-air furnace heat exchanger isn’t like all the other small spots?

Correct! The orange one at the corner of the rectangular exhaust gas flue that’s lit up like the sun, because you’re looking directly into the oil burner flame.
With the fire off and everything cooled down, it looked like this:

Now, this calls for a new furnace (because replacing the heat exchanger costs as much as a new furnace), but as it turns out this was in an unoccupied house during the week before Christmas. So I scrubbed off the debris with a steel brush, bent up a snippet of 2 mil brass shimstock to fit the corner, applied a layer of JB Industro-Weld epoxy to the problem, and positioned 200 W of incandescent bulbs to help it cure slightly sooner than forever:

That is most certainly not a final repair, not just because the heat exchanger’s normal operating temperature exceeds the epoxy’s 500 °F rating, but because where there’s one pinhole there’s bound to be more. The goal was to let us keep the furnace running until we could schedule the replacement after the holidays. Remember, the building isn’t occupied and neither of the smoke / CO detectors went off at any point in the proceedings.
Houses are trouble!