Difficult to say. Doesn't appear to be disease.

If you haven't already done so, pot up, harden off and, when hardened, leave it outdoors.

Thanks for the advice. This is rather a late update but I just wanted to say that soon after I posted this, I potted the tomato in a large container and kept it outside on my apt balcony. The white spots quickly went away on their own. I guess it just needed sunshine and better air circulation!

Looks like pest damage. Some small pests are a bigger problem indoors. When exposed to rain, wind, and predator insects, they decline in population and are no longer a problem.