I've been a power tool mechanic for 18 years now, working at a shop that has been a B&D service center for over 60 years. I collect and restore antique Porter cable tools, myself, but I've repaired my fair share of Black and Decker drills of that era and I would suggest the following:
Make sure you have a grounded cord in good condition. This is critical to safe operation.
Your grease is going to be the consistency of candle wax; scrape it out and replace it. With a drill of that speed, wheel bearing grease will do what you need.
That drill isn't a really high torque tool, but it can and will wrap you up if you aren't careful. Respect it, and pay attention to the moment you break through the material you're drilling. That's the most likely time the drill bit will catch, so ease up.
People seem to think these drills will kill the operator in their sleep, but they are no more dangerous than a circular saw or router, and nothing else is going to drill a big hole in something. Tune it up and use it properly, it's an excellent tool and the machine that put Black and Decker on the map as a manufacturer.
-James Huston