Had anyone been in a situation where you thought one thing and maybe
your electronics were indicating something else?

Pretty much anytime I'm in fog where I can barely see the bow of the boat, I
always "think" one thing; but eventually just stop looking out the window (have
someone else do that for debris) and focus on speed, radar, gps & compass
readings.

What should be the procedure of a MOB in some very bad (limited
visabibility) weather? Assuming you noticed right away, do you react in
time and mark the spot then maneuver for the recovery? I hope to never
have to find out, either as a rescuer or rescuee.

STOP the engines
If you have GPS and it has a MOB feature, hit it.
make a distress call indicating your position, and visibility conditions and
that you're attempting a rescue.
Unless you can actually SEE the person do not motor to where you "think" the MOB
is -- you don't wnat to cut them with the prop or run over them..
LISTEN for their voice or splashes and attempt to make a visual contact.
Dispatch a dingy with attached line & row to where you believe MOB is.

That's what I'd do....