This happened to me (on a 91 - power - defroster mirrors).
 Do you know how to remove the mirror part?  This is
covered in the Bentley manual - Turn the mirror as far to
the side as it will go - look inside for a tongue/flange, (if
not there - turn the mirror the other way and look in the
other side).  Move the flange up (or maybe down) with a
long poker of some sort - it may be hard to move.   Now
with the mirror out you can see the problem.

This was over a year ago, so my memory is a bit fuzzy,
but:  I had no special tools, but I was able to get the nut
back on over the pipe (with wires coming up out of it) and
then with make shift tools - 2 screw-drivers held together
with a tie wrap for leverage - I was able to turn the nut
enough to tighten it and keep the mirror casing in place.
I can't remember if I took the mirror off or not.

If you need more than that - let me know.  The trick is
getting the mirror glass off, then you  can see the
problem and use your ingenuity, or in your case, your
"Tinkerman" skills  :-)  Upon re-reading your email, I feel
that this had been zero help, sorry.  Malcolm

On 2 Oct 2001, at 5:25, TinkerMan wrote:

> The nut securing the bolt serving as the swivel of my
> power mirror's main body to the part attached to the
> door came off. As a result, the mirror swivels freely
> and can't be used properly. I need to get this nut
> back on again, but it seems extremely difficult to do
> so whithout a special tool and without removing the
> mirror completely from the door (difficult for me
> because I've double-secured it from within the door
> with additional nuts against theives). Can anyone
> provide guidance or has previous good experience doing
> this in situ (and how to prevent the nut from coming
> off again)?
>
>
> =====
> Cheers,
>          TinkerMan