spots on leaves of tomato seedlings
These appear to be the cotyledons or seed leaves. Is this spotting also on the "true" leaves?
No it is not on the "true leaves".
The cotyledons ultimately will fall off. I'm not sure what caused the spotting but would not worry about it if the true leaves appear to be healthy.
The problem appears to be a physiological response to the environment rather than a disease. May I assume the seedlings are growing under artificial lights? If so, how close are the lights to the plants?
They were under artificial light until they produced their first true leaf then they were moved out from under the light - the light was 2.5 feet away from them.
Have you examined the undersides of the leaves for possible insect infestation? Also, what is your fertilizer program (what are you using and how concentrated is the solution)?