It looks like a disease for sure, but which one I can't say from these pictures. The spotted leaves could be septoria or one of the bacterial diseases, either spot or speck. Here is a website that may help you ID it: http://vegetablemdonline.ppath.cornell.edu/DiagnosticKeys/TomLeaf/TomLeafKey.html. It would be best to contact your local ag extension agent for a positive diagnosis. You should be able to take them a sample of the leaves and they will positively ID it.

The plant with streaks on the stems is not likely to make it in my opinion, but that's your call. If you have several plants and can stand to pull it, that would be best. But you need to establish whether it's fungal or bacterial so you know what to treat the rest of your tomatoes with as a preventative measure (nothing will cure already diseased foliage). If fungal (and you are not organic), then Daconil is the most effective. If bacterial, copper is the most effective. I usually rotate between the two during the season.

In general when it comes to tomato diseases, remove all diseased leaves as soon as they appear and make sure the plants are mulched heavily so when it rains soil containing the fungal spores isn't splashed on the leaves. Prune all leaves at the bottom of the plant so they are not touching the soil. (Sanitize your pruning shears between plants so you are not spreading any disease.) Get on a preventative maintenance schedule.