My potted tomato plant seems to be diseased. It has black spots on it...?

If the leaves are MISSING, and there are little black kernels at the base of the plant, you have a tomato hornworm. They're exactly the same color as the plant, so you have to look really carefully. It's going to be about as thick as your finger, and probably gripping the underside of a branch somewhere. Go over your whole plant and find it, and kill it.

Yes, you have a virus called black spot. Once it has infested the plant there is no getting rid of it. Usually buying plants that have been bred against some to the viruses and bacteria infections and then treat the plant with either organic or chemical powders that will protect the plant while it is growing.

Might be a bacterial spot, probably from the seeds that have been infected by bacteria. Remove the plant as it might infect the soil as well, and cultivate a healthy soil for next spring. Make sure you fertilize your tomato as well, might make a lot of difference.