Get it out of that pot and in a pot with a drainage hole - otherwise you're going to have many, many, many more black spots. The lack of drainage is slowly killing it. The use of the stones is of no help.

O would agree with Cactus and get in a pot with drainage now! My guess those are patches of rot.

it seems you have been growing this plant quite well. But now is the time to re-pot into something that can drain. Every time you water, build up accumulates in the bottom. It needs to air out and completely dry out.

Stush brings up a good point - when you depot it, let the plant dry out before you repot it, and you might just want to get rid of the old soil (most of it, anyway) and any old, dead roots which are there.

Thank you all! I will definitely repot this plant soon. Glad to hear it doesn't appear to be a disease. I am running out of space in my apartment as I now have about 15 aloes that came from the same initial plant (it came in a small mug!) - and I've given so many to friends and coworkers already! How do you manage crazy aloe growth? How do you maybe slow them down?

Once it's in a suitable pot and soil, don't repot it for a number of years. As to controlling the growth.....make more friends and co-workers, or advertise on Craig's List for free / trade plants? I must admit I've thrown away hundreds of pounds of jade plant myself (but never an Aloe!).

Aloes are basically a desert plant, so hold off the watering and it should go into a more slowdown state. Maybe once a month during cold months and twice during warmer months. If outside during summer you would have to increase water.