Yeah. It is some kind of speck. Probably bacterial.
What I will do is remove the bad ones and thoroughly fungicide, to keep the spread in check. Do it once a week or after any rain again.

Most bacteria need a moist place where air is stagnant to multiply. They cannot survive/thrive in a place with dry moving air. So I would suggest to trim the lower leaves so that the air can move freely under/around the plant.

Sey

Unfortunately pretty much the same problem as most of the other "What is wrong with my plant?" discussions currently running here. So same advice - strip off all affected foliage, bag it and dispose away from the garden, regular spraying program with copper based fungicide since it is bacterial in origin.

Dave

funny... what a huge percentage of tomato problems are bacterial/fungal in nature.