Damping Off: Characterized by a lack of germination or a narrowing of the newly emerged tiny seedlings at the soil line that flop over and die. Various soil fungi are responsible for this condition that are found in any seed starting mix that contains real soil. Also, can be caused by having the plastic that covers your new seedlings tight enough to not permit airflow.
Leggy Seedlings: "Leggy," seedlings means the stems are elongated and limp, flimsy with sparse foliage. Leggy seedlings usually occurs with insufficient or indirect lighting, too much heat, or too much fertilizer. If this occurs for you I suggest you consider repotting the seedlings deeper in your pot, use a fan to improve air circulation and keep temperatures slightly cooler for stockier and hardier plants.
Slow Growth: Have patience. When seedlings seem to be taking forever to grow, it is usually due to low temperatures or inadequate nutrition. Over-watering: Many growers harm their tomato plants by over-watering. Soggy soil may cause your tomato seeds to rot. Once the seedlings have started, they should be watered thoroughly then left un-watered to dry until they are almost ready to wilt, then water them again.
Over-fertilizing: I've seen this often from over-anxious gardeners. Over fertilizing can actually work against your seedlings. This may cause them to stop growing, to grow too rapidly into spindly plants, or even die. One or two applications of very dilute fertilizer are plenty to get a seedling growing to transplant size.