Ignoramus3408 wrote:
I have this Black and Decker 450 RPM drill:

http://igor.chudov.com/tmp/450-rpm-drill.jpg

When plugged into a GFCI outlet, it leaks electricity to ground and
pops the GFCI breaker. The leak is substantial, I believe, however
when plugged into a regular breaker (and handled with caution
appropriate for leaks to case), it actually works and does not blow
the breaker. So, I think, the leak is limited in extent.

To trip a regular breaker, it'd have to be "leaking" 15Amps worth of
electricity.

If you're leaking 15Amps worth of electricity, then the stuff it's
leaking into is being cooked with a couple thousand watts (think
several horsepower worth of power).

GFCI's trip at the few milliamp level (I forget the official number).

Currents as small as 100 microamps can cause heart fibrilation.
Although typically only a fraction of the current flowing through your
hands or feet will go to your heart (I've read a couple of medical
papers where they take fresh cadavers and run electricity through them
sideways, upways, downways, etc, measuring heart current so there must
be some interest in this number.)

My question is, what is the most likely culprit and how to approach
repair of it.

Looking at the picture, grunge grease or dirt in the plug, cable, or
drill body or motor can be enough to trip the GFCI. Looks like somebody
already changed the plug, check it out and make sure they don't
cross-connect neutral with ground (this is guaranteed to trip a GFCI,
unless you've got an open ground connection... the myriad problems with
multiple failure diagnosis!)

What would be the typical application [for this kind of drill]

I hear that California has been having some technical problems with
their method of execution :-).

Timi