Why Tomatoes May Flower ... But Not Set Fruit

My co-worker asked me today if I had any idea why her heirloom tomato plant was flowering and had been for a few weeks, but she had not yet seen fruit start to form.

I wasn't sure, but encouraged her to feed the plant if she hadn't (it's growing in a container, which makes it even more important to fertilize) as a starting point.

I did some research tonight on tomatoes and their fruit-setting ways and found two things, both highlighted in this article from Bonnie Plants, but also noted by other authors: