How many times have you heard the one about how tomatoes are technically a fruit, not a vegetable? This is a great example of something that floats close to being an "urban legend" but doesn't quite fit into the pattern. The truth is, yes, tomatoes are really technically a fruit. They are also a vegetable, and furthermore, they're a berry. None of these things is mutually exclusive with the others.
When you walk down the produce aisle it's easy to assume that "fruit" and "vegetable" are mutually exclusive, and furthermore, that fruits are sweet, and vegetables are not. The word "technically" in the often-cited "fact" suggests that there is some authoritative definition which corroborates the idea that fruits and vegetables are mutually exclusive things, but allows one (and presumably only one) exception to the sweet/savory rule. (Some people even go so far as to imagine that tomatoes fit into fruit only because sometimes they are kind of sweet!)
The word "fruit" does have a technical definition, as supplied by botanists. A fruit is a particular kind of reproductive element of a plant: it contains seeds, and is derived from a flower. Fruits generally include a bit of matter, typically edible, which provide sustenance to the seeds after they germinate. It is common that this material should include sugars because sugars are easy for a plant to make, and a good way to store energy that the seed can use. So an apple is sweet. But most vegetables also contain sugars; they just don't dominate the taste as much, at least as human taste buds detect them, because the proportions and combinations of things that produce flavors are different.
By that definition, not only is a tomato a fruit, so are many of the things we normally consider nuts, and things which contain seeds but are not edible. Amongst the things that are fruit but aren't usually called fruit are gourds (including cucumbers and the various kinds of squash, though pumpkin seems to fall on the border of "fruit" in common parlance since it's often served sweet) and most grains (like corn, rice, and wheat, though admittedly those are pushing it).
Berries are a subset of fruit, in which the fruit is produced from a single ovary. Many things we don't call berries are berries, notably tomatoes, grapes, bananas, and watermelons. Contrariwise, some of our favorite berries, such as blackberries and raspberries, aren't actually berries at all.
The word "vegetable" is less authoritatively defined. In common parlance it just refers to a part of a plant which you can eat, and typically excludes sweet things, though sweet is a fuzzy concept -- there are plenty of edible plant parts which can be sweet or savory depending on how they're prepared or even how they're ripened. The nearest thing we have to a technical definition of "vegetable" is governmental standards regulating import and export, and while these vary from country to country, there's no question that a tomato is a vegetable by any of those rules.
So while people citing the "tomatoes are a fruit" thing are technically correct, the clear implication (sometimes explicitly stated with a clause like "not a vegetable") is incorrect, as is the tacit assumption that these are exclusive. Which means you can't really correct them, even though they're pretty much wrong... and even though it would be fun.
Well, I suppose you could correct them by writing a long-winded blog post about it that no one will read. That, however, wouldn't be anywhere nearly as fun.