Once tomato plants begin to flower and produce fruit, you definitely should fertilize them. Just make sure to avoid high nitrogen products, which can lead to lots of lush, green foliage but little or no fruit formation. Continue fertilizing once or twice a month throughout the growing season.
Espoma Tomato-tone is my go to, but there are others that do the job nicely. 

If you notice flowers falling for no apparent reason, it’s because they aren’t getting pollinated properly. Tomato plants have both male and female flowers and rely primarily on wind to move the pollen from one flower to another. The simple solution is to shake your plants a bit, preferably early in the morning. (This trick works for corn too.) 

Technically, the rot that occurs at the blossom end of developing tomatoes (and peppers, eggplant, squash, even watermelon) is due to a lack of calcium in the soil. But here’s the deal: most soils have plenty of calcium. The real culprit is usually a lack of soil moisture or erratic watering practices, and to a lesser extent, a soil pH below 6.3.

Routine watering and a thick layer of mulch will usually remedy the problem fairly quickly. If you experience the problem year after year, you might also consider adding ground limestone to the soil at planting time both to add calcium and to raise pH. You can also apply products aimed at preventing blossom-end rot, such as Bonide’s Rot-Stop.

Too much water is the main cause of fruit splitting and cracking, which is another reason why routine watering rather than letting the soil remain dry for extended periods is the surest way to prevent it. Cat-Facing is a form of splitting near the stem end of the fruit, but it’s more often seen in cool weather, which affects flower formation and pollination, and is most common on beefsteak and large heirloom tomatoes. As temperatures warm, the condition tends to go away on its own.

Aphids and red spider mites often appear suddenly on tomato stems and foliage, and given their incredible fecundity, both can do serious damage. Spray with Spinosad (such as Captain Jack’s) as soon as you spot them. The tomato hornworm (a rather large and menacing-looking caterpillar) can also do considerable damage. Handpicking (and foot stomping) is the simplest way to get rid of them.

Sadly, tomatoes are prone to a number of diseases -- bacterial, viral, and fungal -- most of which attack the foliage. Often the best defense is to quickly remove any foliage that appears discolored or misshapen. Bacterial and viral diseases can be especially difficult to control, which is why it’s best to purchase resistant varieties. However, many fungal diseases can be controlled with fungicides such as Infuse, Mancozeb, Fung-Onil, and copper-based products.

When daytime temperatures soar into the 90s or remain above 75 degrees overnight, tomatoes struggle to produce fruit, because the excessive heat essentially turns their pollen to mush, which means pollination can’t occur. And sadly, there’s not much you can do about it beyond waiting for cooler temps. Some folks say shade cloth may help a little bit, but I’ve never tried it.

Heat can also slow the ripening of tomatoes, which is why you might consider picking the fruits in the pink stage and letting them finish ripening indoors. They may not be as flavorful, but they’ll still be good. Unfortunately, this trick doesn’t work with cherry tomatoes.

Mushy pollen aside, you can still plant tomatoes in the ground or in containers, and if the weather cooperates you may enjoy a great harvest, especially when temps begin to moderate. And we’ve got great-looking transplants in one- and five-gallon containers.

If you didn’t stake or cage your tomatoes at planting time, you can still do so. Stakes are great for taming overgrown plants, while cages are ideal for newly planted transplants.

Bacon and eggs. Peanut butter and jelly. Bagel and cream cheese. There are dozens of classic two-ingredient dishes. I would add to that list tomatoes and basil (with or without the mozzarella). They not only taste great together, but they grow great together as well. And basil loves warm temperatures.