I would search as much as you can. When you water these plants, are you watering the entire plant, or just the soil? In other words, are the leaves getting wet? If so, you have to look at mildew, mold, fungus as the culprits.

Tomato pests/insects almost always hide on the undersides of leaves and many (aphids, whiteflies) are VERY small. Do you see anything unusual under the leaves of your tomato plants?

Check out these links for pictures to see if these match what you are seeing:
Flea Beetles
Grey Leaf Spot
Bacterial Speck

Quoted from Bachman's:
Whiteflies can be a horrible problem. Look for small white flying insects near the plants and what looks like rice on the bottom side of older leaves. Commercial growers in Florida have been successfully using horticultural oil sprays to smother the eggs and larvae. Slugs munch away at the almost ripe fruit, leaving ragged holes, ruining the tomatoes. Trap and/or repel them as you would with other plants.

Quoted from Bachman's:
Bacterial Speck or Spot produces specking and spotting of both the leaves and fruit. It appears as small raised specks or scabby-looking spots on the fruit, while the leaves may have specking or larger dark spots that lose their centers. If the disease occurs early in the season, the yield may be severely affected. Ripe fruit is unaffected.

Thanks for the reply. I Checked the plants very close and did not see any signs of the bugs or eggs.

The plants are putting out new growth that is green and the
holes are appearing less in the new leave.

Could I have over fertilized, watered, the seedlings? I stopped watering the plants when the mold on the peat pots first showed up. The pots were all soggy and I even transplanted 3 of them. I also used houseplant food at first. The tomatoes seem to be doing ok now.