On plants with thick leaves like aloe, sometimes mite damage looks like that. I get it on my orchids sometimes.
A spray with soapy water will usually nix all the mites. A couple of cc's of dish soap to a liter of water. Spray all surfaces of the plant and the soil surface. Rinse it off before you put it out in the sun. Repeat the treatment in 5 days to a week, to get the next generation - the soap will kill live mites but not eggs.
The spots will not go away but as long as they aren't increasing you know you got rid of the mites. New foliage should come out clean. If you can spray the plant lightly with water a couple of times a week, that will often keep mites away. They hate wet weather.
